diff --git a/clusterview/algorithms.py b/clusterview/algorithms.py
new file mode 100644
index 0000000..ed7f897
--- /dev/null
+++ b/clusterview/algorithms.py
@@ -0,0 +1,120 @@
+from .math import Math
+from .points import Point, PointSet
+
+
+class CentroidGrouping:
+    """
+    A storage class used because Points are not hashable (since the x and y
+    can change). This allows us to do better than just dumping the grouping
+    into a dictionary with a long tuple pointing at an array.
+    """
+    def __init__(self, centroid, points=[]):
+        if not isinstance(centroid, Point):
+            ValueError("Centroid must be a Point.")
+
+        if not isinstance(points, list):
+            ValueError("Points must be in a list.")
+
+        self.__centroid = centroid
+        self.__points = points
+
+    @property
+    def centroid(self):
+        return self.__centroid
+
+    @property
+    def points(self):
+        return self.__points
+
+    def add_point(self, point):
+        """
+        Adds a point.
+
+        @param point The point.
+        """
+
+        if not isinstance(point, Point):
+            raise ValueError("Point must be of type Point.")
+
+        self.__points.append(point)
+
+    def __eq__(self, other):
+        return (self.centroid == other.centroid and
+                self.points == other.points)
+
+
+class Algorithms:
+    """
+    A static class for handling and containing various computational
+    geometry algorithms.
+    """
+
+    # Since all algorithms rely on a set of centroids it is stored here
+    # statically.
+    __centroids = []
+
+    @classmethod
+    def clear_centroids(cls):
+        cls.__centroids = []
+
+    @classmethod
+    def centroids(cls):
+        return cls.__centroids
+
+    @classmethod
+    def set_centroids(cls, centroids):
+        for c in centroids:
+            if not isinstance(c, Point):
+                raise ValueError("Centroids must be of type Point.")
+
+            cls.__centroids.append(c)
+
+    @classmethod
+    def euclidean_grouping(cls, point_set):
+        """
+        Given a point set that EXCLUDES the centroids specified
+        it returns a map from centroid to array of points, where the array
+        of points contains the points with the smallest euclidean distance
+        from that point.
+
+        @param cls The class calling the method.
+        @param point_set The set of points from the UI.
+        """
+        if not isinstance(point_set, PointSet):
+            raise ValueError("Euclidean grouping can only be calculated on " +
+                             "PointSet types.")
+
+        if not cls.__centroids:
+            raise ValueError("No centroids specified.")
+
+        groups = []
+
+        for centroid in cls.__centroids:
+            groups.append(CentroidGrouping(centroid))
+
+        for point in point_set.points:
+            nearest_distance = float("inf")
+            nearest_centroid = None
+
+            for centroid in cls.__centroids:
+                current_distance = Math.euclidean_distance(centroid, point)
+
+                if current_distance < nearest_distance:
+                    nearest_centroid = centroid
+                    nearest_distance = current_distance
+
+            if nearest_centroid is None:
+                raise ValueError("Failed to find centroid nearest " +
+                                 f"to point {point}")
+
+            # We successfully found the nearest centroid to the point
+            # and we can add it to the list.
+            # TODO: Can CentroidGrouping be made hashable?
+            # This is relatively slow for large numbers of groups. If
+            # CentroidGrouping can be made hashable then this becomes O(1).
+            for group in groups:
+                if nearest_centroid == group.centroid:
+                    group.add_point(point)
+                    break
+
+        return groups
diff --git a/clusterview/colors.py b/clusterview/colors.py
index 216e27c..d8adb9c 100644
--- a/clusterview/colors.py
+++ b/clusterview/colors.py
@@ -5,6 +5,9 @@ class Color(str, Enum):
     BLUE = 'BLUE'
     BLACK = 'BLACK'
     GREY = 'GREY'
+    RED = 'RED'
+    ORANGE = 'ORANGE'
+    PURPLE = 'PURPLE'
 
 
 # A simple map from Color -> RGBA 4-Tuple
@@ -13,5 +16,8 @@ class Color(str, Enum):
 COLOR_TO_RGBA = {
     Color.GREY: (0.827, 0.827, 0.826, 0.0),
     Color.BLUE: (0.118, 0.565, 1.0, 0.0),
-    Color.BLACK: (0.0, 0.0, 0.0, 0.0)
+    Color.BLACK: (0.0, 0.0, 0.0, 0.0),
+    Color.RED: (1.0, 0.0, 0.0, 0.0),
+    Color.ORANGE: (0.98, 0.625, 0.12, 0.0),
+    Color.PURPLE: (0.60, 0.40, 0.70, 0.0)
 }
diff --git a/tests/test_algorithms.py b/tests/test_algorithms.py
new file mode 100644
index 0000000..7f90018
--- /dev/null
+++ b/tests/test_algorithms.py
@@ -0,0 +1,89 @@
+import pytest
+
+from clusterview.algorithms import Algorithms, CentroidGrouping
+from clusterview.colors import Color
+from clusterview.points import Point, PointSet
+
+
+@pytest.fixture(autouse=True, scope="function")
+def teardown():
+    """
+    Teardown function for after each test. The current pytest best practice
+    is to run a setup routine, yield, and then run your teardown routine.
+    """
+    yield
+    Algorithms.clear_centroids()
+
+
+def test_empty_centroids():
+    with pytest.raises(ValueError):
+        Algorithms.euclidean_grouping(None)
+
+
+def test_wrong_point_set():
+    centroid_g1 = Point(101, 81, Color.ORANGE, 8, 800, 600)
+    centroid_g2 = Point(357, 222, Color.RED, 8, 800, 600)
+    centroid_g3 = Point(728, 47, Color.PURPLE, 8, 800, 600)
+
+    centroids = [centroid_g1, centroid_g2, centroid_g3]
+
+    Algorithms.set_centroids(centroids)
+
+    with pytest.raises(ValueError):
+        Algorithms.euclidean_grouping(None)
+
+
+def test_euclidean_distance():
+    centroid_g1 = Point(101, 81, Color.ORANGE, 8, 800, 600)
+    centroid_g2 = Point(357, 222, Color.RED, 8, 800, 600)
+    centroid_g3 = Point(728, 47, Color.PURPLE, 8, 800, 600)
+
+    centroids = [centroid_g1, centroid_g2, centroid_g3]
+
+    point1_g1 = Point(67, 59, Color.GREY, 8, 800, 600)
+    point2_g1 = Point(116, 53, Color.GREY, 8, 800, 600)
+    point3_g1 = Point(144, 105, Color.GREY, 8, 800, 600)
+
+    point1_g2 = Point(388, 243, Color.GREY, 8, 800, 600)
+    point2_g2 = Point(358, 248, Color.GREY, 8, 800, 600)
+    point3_g2 = Point(426, 202, Color.GREY, 8, 800, 600)
+
+    point1_g3 = Point(750, 47, Color.GREY, 8, 800, 600)
+    point2_g3 = Point(741, 85, Color.GREY, 8, 800, 600)
+    point3_g3 = Point(700, 72, Color.GREY, 8, 800, 600)
+
+    # This PointSet is the PointSet that excludes the centroids.
+    point_set = PointSet(8, 800, 600)
+    point_set.add_point(67, 59, Color.GREY)
+    point_set.add_point(116, 53, Color.GREY)
+    point_set.add_point(144, 105, Color.GREY)
+
+    point_set.add_point(388, 243, Color.GREY)
+    point_set.add_point(358, 248, Color.GREY)
+    point_set.add_point(426, 202, Color.GREY)
+
+    point_set.add_point(750, 47, Color.GREY)
+    point_set.add_point(741, 85, Color.GREY)
+    point_set.add_point(700, 72, Color.GREY)
+
+    centroid_grouping_1 = CentroidGrouping(centroid_g1,
+                                           [point1_g1, point2_g1, point3_g1])
+
+    centroid_grouping_2 = CentroidGrouping(centroid_g2,
+                                           [point1_g2, point2_g2, point3_g2])
+
+    centroid_grouping_3 = CentroidGrouping(centroid_g3,
+                                           [point1_g3, point2_g3, point3_g3])
+
+    expected = [centroid_grouping_1, centroid_grouping_2, centroid_grouping_3]
+
+    Algorithms.set_centroids(centroids)
+    actual = Algorithms.euclidean_grouping(point_set)
+
+    assert len(actual) == len(expected)
+
+    # Since I don't want to figure out what grouping is where I'll accept
+    # the linearity of `in`.
+    assert centroid_grouping_1 in actual
+    assert centroid_grouping_2 in actual
+    assert centroid_grouping_3 in actual