| The essential dimension of an algebraic structure is the number of independent parameters needed to describe it up to isomorphism. We will motivate the study of this invariant by relating it to some open conjectures in algebra and number theory, and will explain why the computation of the essential dimension of homogeneous forms is particularly relevant. We then introduce a new invariant, namely the canonical dimension, and relate it to the computation of essential dimension of homogeneous forms. We will then compute it in several cases. |