Our main objective in this thesis is to contribute to the understanding and improvement of equivariance in neural network models. In terms of applications, we focus on handshape classification for sign language and other types of gestures using convolutional networks. Therefore, we set the following specific goals: • Analyze CNN models design specifically for equivariance • Compare specific models and data augmentation as means to obtain equivariance. Evaluate transfer learning strategies to obtain equivariant models starting with non-equivariant ones. • Develop equivariance measures for activations or inner representations in Neural Networks. Implement those measures in an open source library. Analyze the measures behavior, and compare with existing measures.Facultad de Informática