In this book, Professor Novikov describes recent developments in soliton theory and their relations to so-called Poisson geometry. This formalism, which is related to symplectic geometry, is extremely useful for the study of integrable systems that are described in terms of differential equations (ordinary or partial) and quantum field theories. Professor Novikov examines several Hamiltonian systems, within the framework of Poisson geometry, to demonstrate its power. This book will be of interest to mathematicians and physicists.