diff --git a/prototorch/core/transforms.py b/prototorch/core/transforms.py
new file mode 100644
index 0000000..3a0ded2
--- /dev/null
+++ b/prototorch/core/transforms.py
@@ -0,0 +1,44 @@
+"""ProtoTorch transforms"""
+
+import torch
+from torch.nn.parameter import Parameter
+
+from .initializers import (
+    AbstractLinearTransformInitializer,
+    EyeTransformInitializer,
+)
+
+
+class LinearTransform(torch.nn.Module):
+    def __init__(
+            self,
+            in_dim: int,
+            out_dim: int,
+            initializer:
+        AbstractLinearTransformInitializer = EyeTransformInitializer(),
+            **kwargs):
+        super().__init__(**kwargs)
+        self.set_weights(in_dim, out_dim, initializer)
+
+    @property
+    def weights(self):
+        return self._weights.detach().cpu()
+
+    def _register_weights(self, weights):
+        self.register_parameter("_weights", Parameter(weights))
+
+    def set_weights(
+        self,
+        in_dim: int,
+        out_dim: int,
+        initializer:
+        AbstractLinearTransformInitializer = EyeTransformInitializer()):
+        weights = initializer.generate(in_dim, out_dim)
+        self._register_weights(weights)
+
+    def forward(self, x):
+        return x @ self.weights.T
+
+
+# Aliases
+Omega = LinearTransform