diff --git a/docs/source/links.rst b/docs/source/links.rst
index e39f37bb7ea..5a199b4d4c2 100644
--- a/docs/source/links.rst
+++ b/docs/source/links.rst
@@ -142,3 +142,7 @@
 .. _Equal opportunity: https://proceedings.neurips.cc/paper/2016/hash/9d2682367c3935defcb1f9e247a97c0d-Abstract.html
 .. _Seamless Scene Segmentation paper: https://arxiv.org/abs/1905.01220
 .. _Fleiss kappa: https://en.wikipedia.org/wiki/Fleiss%27_kappa
+.. _CIOU: https://arxiv.org/abs/2005.03572
+.. _DIOU: https://arxiv.org/abs/1911.08287v1
+.. _GIOU: https://arxiv.org/abs/1902.09630
+.. _pycocotools: https://github.com/cocodataset/cocoapi/tree/master/PythonAPI/pycocotools
diff --git a/src/torchmetrics/aggregation.py b/src/torchmetrics/aggregation.py
index d15325fedbe..5042a2f3877 100644
--- a/src/torchmetrics/aggregation.py
+++ b/src/torchmetrics/aggregation.py
@@ -657,7 +657,7 @@ def __init__(
 class RunningSum(Running):
     """Aggregate a stream of value into their sum over a running window.
 
-    Using this metric compared to `MeanMetric` allows for calculating metrics over a running window of values, instead
+    Using this metric compared to `SumMetric` allows for calculating metrics over a running window of values, instead
     of the whole history of values. This is beneficial when you want to get a better estimate of the metric during
     training and don't want to wait for the whole training to finish to get epoch level estimates.
 
diff --git a/src/torchmetrics/audio/sdr.py b/src/torchmetrics/audio/sdr.py
index c2bf6d00bb9..23026ca177b 100644
--- a/src/torchmetrics/audio/sdr.py
+++ b/src/torchmetrics/audio/sdr.py
@@ -168,11 +168,11 @@ class ScaleInvariantSignalDistortionRatio(Metric):
     As input to `forward` and `update` the metric accepts the following input
 
     - ``preds`` (:class:`~torch.Tensor`): float tensor with shape ``(...,time)``
-    - ``target`` (: :class:`~torch.Tensor`): float tensor with shape ``(...,time)``
+    - ``target`` (:class:`~torch.Tensor`): float tensor with shape ``(...,time)``
 
     As output of `forward` and `compute` the metric returns the following output
 
-    - ``si_sdr`` (: :class:`~torch.Tensor`): float scalar tensor with average SI-SDR value over samples
+    - ``si_sdr`` (:class:`~torch.Tensor`): float scalar tensor with average SI-SDR value over samples
 
     Args:
         zero_mean: if to zero mean target and preds or not
diff --git a/src/torchmetrics/audio/snr.py b/src/torchmetrics/audio/snr.py
index 8954914ebf9..b1ed39d3055 100644
--- a/src/torchmetrics/audio/snr.py
+++ b/src/torchmetrics/audio/snr.py
@@ -145,11 +145,11 @@ class ScaleInvariantSignalNoiseRatio(Metric):
     As input to `forward` and `update` the metric accepts the following input
 
     - ``preds`` (:class:`~torch.Tensor`): float tensor with shape ``(...,time)``
-    - ``target`` (: :class:`~torch.Tensor`): float tensor with shape ``(...,time)``
+    - ``target`` (:class:`~torch.Tensor`): float tensor with shape ``(...,time)``
 
     As output of `forward` and `compute` the metric returns the following output
 
-    - ``si_snr`` (: :class:`~torch.Tensor`): float scalar tensor with average SI-SNR value over samples
+    - ``si_snr`` (:class:`~torch.Tensor`): float scalar tensor with average SI-SNR value over samples
 
     Args:
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
@@ -241,15 +241,15 @@ class ComplexScaleInvariantSignalNoiseRatio(Metric):
 
     As input to `forward` and `update` the metric accepts the following input
 
-    - ``preds`` (:class:`~torch.Tensor`): real/complex float tensor with shape ``(..., frequency, time, 2)``\
-        / ``(..., frequency, time)``
+    - ``preds`` (:class:`~torch.Tensor`): real float tensor with shape ``(...,frequency,time,2)`` or complex float
+      tensor with shape ``(..., frequency,time)``
 
-    - ``target`` (: :class:`~torch.Tensor`): real/complex float tensor with shape ``(..., frequency, time, 2)``\
-        / ``(..., frequency, time)``
+    - ``target`` (:class:`~torch.Tensor`): real float tensor with shape ``(...,frequency,time,2)`` or complex float
+      tensor with shape ``(..., frequency,time)``
 
     As output of `forward` and `compute` the metric returns the following output
 
-    - ``c_si_snr`` (: :class:`~torch.Tensor`): float scalar tensor with average C-SI-SNR value over samples
+    - ``c_si_snr`` (:class:`~torch.Tensor`): float scalar tensor with average C-SI-SNR value over samples
 
     Args:
         zero_mean: if to zero mean target and preds or not
diff --git a/src/torchmetrics/detection/_mean_ap.py b/src/torchmetrics/detection/_mean_ap.py
index 31ad5d6af06..b24a6ba8eaf 100644
--- a/src/torchmetrics/detection/_mean_ap.py
+++ b/src/torchmetrics/detection/_mean_ap.py
@@ -210,9 +210,8 @@ class MeanAveragePrecision(Metric):
         The default properties are also accessible via fields and will raise an ``AttributeError`` if not available.
 
     .. note::
-        This metric is following the mAP implementation of
-        `pycocotools <https://github.com/cocodataset/cocoapi/tree/master/PythonAPI/pycocotools>`_,
-        a standard implementation for the mAP metric for object detection.
+        This metric is following the mAP implementation of `pycocotools`_ a standard implementation for the mAP metric
+        for object detection.
 
     .. note::
         This metric requires you to have `torchvision` version 0.8.0 or newer installed
diff --git a/src/torchmetrics/detection/ciou.py b/src/torchmetrics/detection/ciou.py
index f967a449b8c..8197fa2e5b1 100644
--- a/src/torchmetrics/detection/ciou.py
+++ b/src/torchmetrics/detection/ciou.py
@@ -27,7 +27,7 @@
 
 
 class CompleteIntersectionOverUnion(IntersectionOverUnion):
-    r"""Computes Complete Intersection Over Union (CIoU) <https://arxiv.org/abs/2005.03572>`_.
+    r"""Computes Complete Intersection Over Union (`CIoU`_).
 
     As input to ``forward`` and ``update`` the metric accepts the following input:
 
@@ -55,7 +55,7 @@ class CompleteIntersectionOverUnion(IntersectionOverUnion):
     - ``ciou_dict``: A dictionary containing the following key-values:
 
         - ciou: (:class:`~torch.Tensor`)
-        - ciou/cl_{cl}: (:class:`~torch.Tensor`), if argument ``class metrics=True``
+        - ciou/cl_{cl}: (:class:`~torch.Tensor`), if argument ``class_metrics=True``
 
     Args:
         box_format:
diff --git a/src/torchmetrics/detection/diou.py b/src/torchmetrics/detection/diou.py
index f30ef869ec2..65724cf8a41 100644
--- a/src/torchmetrics/detection/diou.py
+++ b/src/torchmetrics/detection/diou.py
@@ -27,7 +27,7 @@
 
 
 class DistanceIntersectionOverUnion(IntersectionOverUnion):
-    r"""Computes Distance Intersection Over Union (DIoU) <https://arxiv.org/abs/1911.08287v1>`_.
+    r"""Computes Distance Intersection Over Union (`DIoU`_).
 
     As input to ``forward`` and ``update`` the metric accepts the following input:
 
@@ -55,7 +55,7 @@ class DistanceIntersectionOverUnion(IntersectionOverUnion):
     - ``diou_dict``: A dictionary containing the following key-values:
 
         - diou: (:class:`~torch.Tensor`)
-        - diou/cl_{cl}: (:class:`~torch.Tensor`), if argument ``class metrics=True``
+        - diou/cl_{cl}: (:class:`~torch.Tensor`), if argument ``class_metrics=True``
 
     Args:
         box_format:
diff --git a/src/torchmetrics/detection/giou.py b/src/torchmetrics/detection/giou.py
index e06660ea751..8d3393b9f89 100644
--- a/src/torchmetrics/detection/giou.py
+++ b/src/torchmetrics/detection/giou.py
@@ -27,7 +27,7 @@
 
 
 class GeneralizedIntersectionOverUnion(IntersectionOverUnion):
-    r"""Compute Generalized Intersection Over Union (GIoU) <https://arxiv.org/abs/1902.09630>`_.
+    r"""Compute Generalized Intersection Over Union (`GIoU`_).
 
     As input to ``forward`` and ``update`` the metric accepts the following input:
 
@@ -90,6 +90,7 @@ class GeneralizedIntersectionOverUnion(IntersectionOverUnion):
     Raises:
         ModuleNotFoundError:
             If torchvision is not installed with version 0.8.0 or newer.
+
     """
     _iou_type: str = "giou"
     _invalid_val: float = -1.0
diff --git a/src/torchmetrics/detection/panoptic_qualities.py b/src/torchmetrics/detection/panoptic_qualities.py
index a913826af6b..0dde6eb9537 100644
--- a/src/torchmetrics/detection/panoptic_qualities.py
+++ b/src/torchmetrics/detection/panoptic_qualities.py
@@ -36,12 +36,12 @@
 class PanopticQuality(Metric):
     r"""Compute the `Panoptic Quality`_ for panoptic segmentations.
 
-        .. math::
-            PQ = \frac{IOU}{TP + 0.5 FP + 0.5 FN}
+    .. math::
+        PQ = \frac{IOU}{TP + 0.5 FP + 0.5 FN}
 
-        where IOU, TP, FP and FN are respectively the sum of the intersection over union for true positives,
-        the number of true postitives, false positives and false negatives. This metric is inspired by the PQ
-        implementation of panopticapi, a standard implementation for the PQ metric for panoptic segmentation.
+    where IOU, TP, FP and FN are respectively the sum of the intersection over union for true positives,
+    the number of true postitives, false positives and false negatives. This metric is inspired by the PQ
+    implementation of panopticapi, a standard implementation for the PQ metric for panoptic segmentation.
 
     .. note:
         Points in the target tensor that do not map to a known category ID are automatically ignored in the metric
@@ -224,8 +224,8 @@ class ModifiedPanopticQuality(Metric):
     .. math::
         PQ^{\dagger}_c = \frac{IOU_c}{|S_c|}
 
-    where IOU_c is the sum of the intersection over union of all matching segments for a given class, and \|S_c| is
-    the overall number of segments in the ground truth for that class.
+    where :math:`IOU_c` is the sum of the intersection over union of all matching segments for a given class, and
+    :math:`|S_c|` is the overall number of segments in the ground truth for that class.
 
     .. note:
         Points in the target tensor that do not map to a known category ID are automatically ignored in the metric
diff --git a/src/torchmetrics/functional/audio/snr.py b/src/torchmetrics/functional/audio/snr.py
index 08c2880aecc..db15c0a8b3f 100644
--- a/src/torchmetrics/functional/audio/snr.py
+++ b/src/torchmetrics/functional/audio/snr.py
@@ -89,8 +89,10 @@ def complex_scale_invariant_signal_noise_ratio(preds: Tensor, target: Tensor, ze
     """`Complex scale-invariant signal-to-noise ratio`_ (C-SI-SNR).
 
     Args:
-        preds: real/complex float tensor with shape ``(..., frequency, time, 2)``/``(..., frequency, time)``
-        target: real/complex float tensor with shape ``(..., frequency, time, 2)``/``(..., frequency, time)``
+        preds: real float tensor with shape ``(...,frequency,time,2)`` or complex float tensor with
+            shape ``(..., frequency,time)``
+        target: real float tensor with shape ``(...,frequency,time,2)`` or complex float tensor with
+            shape ``(..., frequency,time)``
         zero_mean: When set to True, the mean of all signals is subtracted prior to computation of the metrics
 
     Returns:
@@ -98,7 +100,7 @@ def complex_scale_invariant_signal_noise_ratio(preds: Tensor, target: Tensor, ze
 
     Raises:
         RuntimeError:
-            If ``preds`` is not the shape (..., frequency, time, 2) (after being converted to real if it is complex).
+            If ``preds`` is not the shape (...,frequency,time,2) (after being converted to real if it is complex).
             If ``preds`` and ``target`` does not have the same shape.
 
     Example:
diff --git a/src/torchmetrics/functional/detection/ciou.py b/src/torchmetrics/functional/detection/ciou.py
index f1f340f6726..d0f5533b802 100644
--- a/src/torchmetrics/functional/detection/ciou.py
+++ b/src/torchmetrics/functional/detection/ciou.py
@@ -48,7 +48,7 @@ def complete_intersection_over_union(
     replacement_val: float = 0,
     aggregate: bool = True,
 ) -> torch.Tensor:
-    r"""Compute `Complete Intersection over Union <https://arxiv.org/abs/2005.03572>`_ between two sets of boxes.
+    r"""Compute Complete Intersection over Union (`CIOU`_) between two sets of boxes.
 
     Both sets of boxes are expected to be in (x1, y1, x2, y2) format with 0 <= x1 < x2 and 0 <= y1 < y2.
 
@@ -71,6 +71,7 @@ def complete_intersection_over_union(
         >>> target = torch.Tensor([[110, 110, 210, 210]])
         >>> complete_intersection_over_union(preds, target)
         tensor(0.6724)
+
     """
     if not _TORCHVISION_GREATER_EQUAL_0_13:
         raise ModuleNotFoundError(
diff --git a/src/torchmetrics/functional/detection/diou.py b/src/torchmetrics/functional/detection/diou.py
index 8cb641a00ec..42554df0f20 100644
--- a/src/torchmetrics/functional/detection/diou.py
+++ b/src/torchmetrics/functional/detection/diou.py
@@ -48,7 +48,7 @@ def distance_intersection_over_union(
     replacement_val: float = 0,
     aggregate: bool = True,
 ) -> torch.Tensor:
-    r"""Compute `Distance Intersection over Union <https://arxiv.org/abs/1911.08287v1>`_ between two sets of boxes.
+    r"""Compute Distance Intersection over Union (`DIOU`_) between two sets of boxes.
 
     Both sets of boxes are expected to be in (x1, y1, x2, y2) format with 0 <= x1 < x2 and 0 <= y1 < y2.
 
@@ -71,6 +71,7 @@ def distance_intersection_over_union(
         >>> target = torch.Tensor([[110, 110, 210, 210]])
         >>> distance_intersection_over_union(preds, target)
         tensor(0.6724)
+
     """
     if not _TORCHVISION_GREATER_EQUAL_0_13:
         raise ModuleNotFoundError(
diff --git a/src/torchmetrics/functional/detection/giou.py b/src/torchmetrics/functional/detection/giou.py
index a46ab8ef99b..980784f7e4f 100644
--- a/src/torchmetrics/functional/detection/giou.py
+++ b/src/torchmetrics/functional/detection/giou.py
@@ -48,7 +48,7 @@ def generalized_intersection_over_union(
     replacement_val: float = 0,
     aggregate: bool = True,
 ) -> torch.Tensor:
-    r"""Compute `Generalized Intersection over Union <https://arxiv.org/abs/1902.09630>`_ between two sets of boxes.
+    r"""Compute Generalized Intersection over Union (`GIOU`_) between two sets of boxes.
 
     Both sets of boxes are expected to be in (x1, y1, x2, y2) format with 0 <= x1 < x2 and 0 <= y1 < y2.
 
@@ -71,6 +71,7 @@ def generalized_intersection_over_union(
         >>> target = torch.Tensor([[110, 110, 210, 210]])
         >>> generalized_intersection_over_union(preds, target)
         tensor(0.6641)
+
     """
     if not _TORCHVISION_GREATER_EQUAL_0_8:
         raise ModuleNotFoundError(
diff --git a/src/torchmetrics/functional/detection/panoptic_qualities.py b/src/torchmetrics/functional/detection/panoptic_qualities.py
index 6fcb14960e1..e30c29555b7 100644
--- a/src/torchmetrics/functional/detection/panoptic_qualities.py
+++ b/src/torchmetrics/functional/detection/panoptic_qualities.py
@@ -43,7 +43,6 @@ def panoptic_quality(
     true postitives, false positives and false negatives. This metric is inspired by the PQ implementation of
     panopticapi, a standard implementation for the PQ metric for object detection.
 
-
     .. note:
         Points in the target tensor that do not map to a known category ID are automatically ignored in the metric
         computation.
@@ -120,8 +119,8 @@ def modified_panoptic_quality(
     .. math::
         PQ^{\dagger}_c = \frac{IOU_c}{|S_c|}
 
-    where IOU_c is the sum of the intersection over union of all matching segments for a given class, and \|S_c| is
-    the overall number of segments in the ground truth for that class.
+    where :math:`IOU_c` is the sum of the intersection over union of all matching segments for a given class, and
+    :math:`|S_c|` is the overall number of segments in the ground truth for that class.
 
     .. note:
         Points in the target tensor that do not map to a known category ID are automatically ignored in the metric
@@ -151,7 +150,7 @@ def modified_panoptic_quality(
         TypeError:
             If ``preds`` or ``target`` is not an ``torch.Tensor``.
         ValueError:
-             If ``preds`` or ``target`` has different shape.
+            If ``preds`` or ``target`` has different shape.
         ValueError:
             If ``preds`` has less than 3 dimensions.
         ValueError:
diff --git a/src/torchmetrics/image/fid.py b/src/torchmetrics/image/fid.py
index 2afbc62db0c..879e305771c 100644
--- a/src/torchmetrics/image/fid.py
+++ b/src/torchmetrics/image/fid.py
@@ -191,8 +191,8 @@ class FrechetInceptionDistance(Metric):
     The metric was originally proposed in `fid ref1`_.
 
     Using the default feature extraction (Inception v3 using the original weights from `fid ref2`_), the input is
-    expected to be mini-batches of 3-channel RGB images of shape ``(3 x H x W)``. If argument ``normalize``
-    is ``True`` images are expected to be dtype ``float`` and have values in the ``[0, 1]`` range, else if
+    expected to be mini-batches of 3-channel RGB images of shape ``(3xHxW)``. If argument ``normalize``
+    is ``True`` images are expected to be dtype ``float`` and have values in the ``[0,1]`` range, else if
     ``normalize`` is set to ``False`` images are expected to have dtype ``uint8`` and take values in the ``[0, 255]``
     range. All images will be resized to 299 x 299 which is the size of the original training data. The boolian
     flag ``real`` determines if the images should update the statistics of the real distribution or the
diff --git a/src/torchmetrics/image/inception.py b/src/torchmetrics/image/inception.py
index 5aa39d09490..8b2885081af 100644
--- a/src/torchmetrics/image/inception.py
+++ b/src/torchmetrics/image/inception.py
@@ -44,8 +44,8 @@ class InceptionScore(Metric):
     `inception ref1`_.
 
     Using the default feature extraction (Inception v3 using the original weights from `inception ref2`_), the input
-    is expected to be mini-batches of 3-channel RGB images of shape ``(3 x H x W)``. If argument ``normalize``
-    is ``True`` images are expected to be dtype ``float`` and have values in the ``[0, 1]`` range, else if
+    is expected to be mini-batches of 3-channel RGB images of shape ``(3xHxW)``. If argument ``normalize``
+    is ``True`` images are expected to be dtype ``float`` and have values in the ``[0,1]`` range, else if
     ``normalize`` is set to ``False`` images are expected to have dtype uint8 and take values in the ``[0, 255]``
     range. All images will be resized to 299 x 299 which is the size of the original training data.
 
diff --git a/src/torchmetrics/image/kid.py b/src/torchmetrics/image/kid.py
index 84cfd198191..5fbcf0ac68b 100644
--- a/src/torchmetrics/image/kid.py
+++ b/src/torchmetrics/image/kid.py
@@ -84,8 +84,8 @@ class KernelInceptionDistance(Metric):
     subsets to be able to both get the mean and standard deviation of KID.
 
     Using the default feature extraction (Inception v3 using the original weights from `kid ref2`_), the input is
-    expected to be mini-batches of 3-channel RGB images of shape ``(3 x H x W)``. If argument ``normalize``
-    is ``True`` images are expected to be dtype ``float`` and have values in the ``[0, 1]`` range, else if
+    expected to be mini-batches of 3-channel RGB images of shape ``(3xHxW)``. If argument ``normalize``
+    is ``True`` images are expected to be dtype ``float`` and have values in the ``[0,1]`` range, else if
     ``normalize`` is set to ``False`` images are expected to have dtype ``uint8`` and take values in the ``[0, 255]``
     range. All images will be resized to 299 x 299 which is the size of the original training data. The boolian
     flag ``real`` determines if the images should update the statistics of the real distribution or the
diff --git a/src/torchmetrics/image/ssim.py b/src/torchmetrics/image/ssim.py
index b34c60cc893..50b36172afc 100644
--- a/src/torchmetrics/image/ssim.py
+++ b/src/torchmetrics/image/ssim.py
@@ -228,7 +228,7 @@ class MultiScaleStructuralSimilarityIndexMeasure(Metric):
 
     As output of `forward` and `compute` the metric returns the following output
 
-    - ``msssim`` (: :class:`~torch.Tensor`): if ``reduction!='none'`` returns float scalar tensor with average MSSSIM
+    - ``msssim`` (:class:`~torch.Tensor`): if ``reduction!='none'`` returns float scalar tensor with average MSSSIM
       value over sample else returns tensor of shape ``(N,)`` with SSIM values per sample
 
     Args:
diff --git a/src/torchmetrics/regression/minkowski.py b/src/torchmetrics/regression/minkowski.py
index 7563cb4b270..9921ce0e326 100644
--- a/src/torchmetrics/regression/minkowski.py
+++ b/src/torchmetrics/regression/minkowski.py
@@ -29,16 +29,17 @@
 class MinkowskiDistance(Metric):
     r"""Compute `Minkowski Distance`_.
 
-    .. math:: d_{\text{Minkowski}} = \\sum_{i}^N (| y_i - \\hat{y_i} |^p)^\frac{1}{p}
+    .. math::
+        d_{\text{Minkowski}} = \sum_{i}^N (| y_i - \hat{y_i} |^p)^\frac{1}{p}
+
+    where
+        :math: `y` is a tensor of target values,
+        :math: `\hat{y}` is a tensor of predictions,
+        :math: `\p` is a non-negative integer or floating-point number
 
     This metric can be seen as generalized version of the standard euclidean distance which corresponds to minkowski
     distance with p=2.
 
-    where
-        :math:`y` is a tensor of target values,
-        :math:`\\hat{y}` is a tensor of predictions,
-        :math: `\\p` is a non-negative integer or floating-point number
-
     Args:
         p: int or float larger than 1, exponent to which the difference between preds and target is to be raised
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.