This book provides a comprehensive collection of problems together with their detailed solutions in the field of Theoretical and Mathematical Physics. All modern fields in Theoretical and Mathematical Physics are covered. It is the only book which covers all the new techniques and methods in theoretical and mathematical physics. Third edition updated with: Exercises in: Hilbert space theory, Lie groups, Matrix-valued differential forms, and Bose-Fermi operators and string theory. All other chapters have been updated with new problems and materials. Most chapters contain an introduction to the subject discussed in the text.

Groups Kronecker and Tensor Products Nambu Mechanics Gateaux and Fréchet Derivatives Stability and Bifurcations Nonlinear Ordinary Difference Equations Nonlinear Ordinary Differential Equations Lax Representations in Classical Mechanics Hilbert Spaces Generalized Functions Linear Partial Differential Equations Nonlinear Partial Differential Equations Symmetries and Group Theoretical Reductions Soliton Equations Lax Pairs for Partial Differential Equations Bäcklund Transformations Hirota Technique Painlevé Test Lie Algebras Lie Groups Differential Forms Matrix-Valued Differential Forms Lie Derivative Metric Tensor Fields Killing Vector Fields Inequalities Ising Model and Heisenberg Model Number Theory Combinatorial Problems Fermi Operators Bose Operators Bose-Fermi Systems Lax Representations and Bethe Ansatz Gauge Transformations Chaos, Fractals and Complexity