In this volume, the author exposes the basic techniques of using Lie algebraic concepts to explore the domain of nonlinear integrable systems. The emphasis is not on developing a rigorous mathematical basis, but on using Lie algebraic methods as an effective tool.

This volume examines the basic techniques of using Lie algebraic concepts to explore the domain of nonlinear integrable systems. It provides a comprehensive treatment of Lie methods and summarizes their use in various fields of theoretical research.

Lie algebra
prolongation theory
co-adjoint orbits
symmetries of integrable systems
Hamiltonian structure
classical r-matrix.