Reduction Principles

This text contains lecture notes to the series of lectures delivered at the C.I.M.E. course “Geometric and analytic aspects of functional variational principles” held in Cetraro (Cosenza), June 27–June 1, 2022. I am very indebted to Paolo Salani and also to the Scientific Directors Andrea Cianchi, Vladimir Maz’ya and Tobias Weth for the very kind invitation. Delivering a course on a legendary C.I.M.E. school was a great honor and immense pleasure for me.