The second edition of "Advanced Methods of Mathematical Physics" has been considerably revised, enlarged and updated. This is typically a two-semester course material for students pursuing Master's degree programs in theoretical physics and mathematics covering such topics as the theory of finite groups, introductory topology and differential geometry, integral equations, Sturm-Liouvilles's theory including Green's functions, stochastic processes and stochastic differential equations, nonlinear dynamics, solution of nonlinear differential and integral equations, symmetries of differential equations and normal modes in nonlinear dynamical systems. What the anvil means to the blacksmith, what a car means to the businessman, what a violin means to the musician, that's what mathematics means to a theoretical physicist. Not only can we not live without it. We love mathematics. We play with it even in the rare cases that we do not need it. Mathematics is fun. Students in theoretical physics need good teachers and good books to learn mathematics. Here is such a book. "Devour. Enjoy". (Gerardus 't Hooft Noble Laureate Professor of Physics, University of Utrecht, The Netherlands). "An extremely useful textbook. I am sure that it will be much used by many students." (James D. Bjorken Professor of Physics, Stanford Linear Accelerator Center, Stanford University, USA). New to the Second Edition: two appendices: on differentiation and integration under the integral sign; and on the existence of the limit cycles in a Lienard system. New examples as also some additional pertinent problems listed at appropriate places in the text.
