It is divided into three parts, covering Hamiltonian systems, Riemannian geometry and calculus of variations, and topology. The range of applications of these topics is very broad, as many modern geometrical problems recur across a wide range of fields, including mechanics and physics as well as mathematics. Many of the approaches to problems presented in this volume will be novel to the Western reader, although questions are of global interest. The main achievements of the Russian school are placed in the context of the development of each individual subject.

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