The essential dimension of an algebraic object is the minimal number of independent parameters one needs to define it. This notion was initially introduced in the context where the objects in question are finite field extensions. Essential dimension has since been investigated in several broader contexts, by a range of techniques, and has been found to have interesting and surprising connections to many problems in algebra and algebraic geometry. The course will survey some of this research. It will be started with the definition of essential

dimension and conclude with a discussion of open problems.

The course will survey some of this research. It will be started with the definition of essential dimension and conclude with a discussion of open problems.