This 10-hour course will take place at the Basque Center for Applied Mathematics (Bilbao), Spain, from Monday, May 19th to Friday, May 23rd, from 10:00-12:00.

An overview of diverse optimal embeddings for Orlicz-Sobolev spaces will be offered. Orlicz-Sobolev embeddings into Orlicz spaces, Orlicz-Lorentz spaces, and spaces of continuous functions will be presented. Trace embeddings will also be considered. The role of these embeddings in some regularity results for solutions to nonlinear elliptic partial differential equations and problems of the calculus of variations under growth conditions of non-polynomial type will be described.