This course focuses on computational methods in cryo-EM with special emphasis on methods that play a significant role in many other inverse problems and data science applications and to their mathematical foundation. These comprise of key elements of statistical inference, image processing, optimization, and dimension reduction. Methods include rotation estimation and three-dimensional ab-initio modelling, structure refinement, resolving structural variability of heterogeneous populations, derivation of the image formation model, model validation, and resolution determination.