Symplectic and contact forms are objects which arose originally in classical mechanics, but have recently been studied for their own sake.

I will explain what they are, where they come from, and how they relate to other objects (especially Riemannian metrics). Kahler structures, complex and almost complex structures, Sasakian structures, etc., are all related to these.

In addition, I will describe the groups of diffeomorphisms which preserve these structures, and what geodesics on such groups look like.

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