A collection of five surveys on dynamical systems, indispensable for graduate students and researchers in mathematics and theoretical physics. Written in the modern language of differential geometry, the book covers all the new differential geometric and Lie-algebraic methods currently used in the theory of integrable systems.

Translated by: A.G. Reyman, M.A. Semenov-Tian-Shansky
Contributions by: A.T. Fomenko, V.Ya. Gershkovich, M.A. Olshanetsky, A.M. Perelomov, A.G. Rejman, M.A. Semenov-Tian-Shansky, V.V. Trofimov, A.M. Vershik