This lecture and tutorial introduces the invariant variational autoencoders (rotation, translation) and extentions to conditional, joint, and semi-supervised architectures. The GitHub repository contains examples of the VAE for imaging data (cards, graphene) and spectroscopy (EELS of plasmonic structures). The repo is: https://github.com/SergeiVKalinin/ML-ElectronMicroscopy-2023/tree/main/Lecture%2017