The Group equivariant Convolutional Neural Network (G-CNN) is a new kind of neural network that obtains better sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that enjoys a substantially higher degree of weight sharing than regular convolution layers. G-convolutions increase the expressive capacity of the network without increasing the number of parameters, are easy to use, and can be implemented with negligible computational overhead for discrete groups generated by translations, reflections and rotations. G-CNNs achieve state of the art results on CIFAR10 and rotated MNIST. In this talk we will briefly discuss the basics of symmetry groups and their relation to computer vision and machine learning, and then present the theory and practice of G-CNNs in a mathematical and visual manner. No prior knowledge of group theory is required.