Mathematical Physics: Advanced Topics is the second of the two-volume set on mathematical physics by the author. In volume 1, Mathematical Physics: The Basics, topics such as vectors and tensors, curvilinear coordinates, linear vector spaces and operators, and complex variables and their applications were covered. This book addresses the more advanced topics: partial differential equations, ordinary differential equations, special functions including gamma, beta and Bessel functions, classical orthogonal polynomials and spherical harmonics. It also includes generalized functions, the Dirac-delta function, Fourier transforms and a brief introduction to group theory. A large number of solved problems and exercises have been included in each chapter. Together with Mathematical Physics: The Basics, this book will serve as a comprehensive textbook for M.Sc. and Ph.D. students of physics and chemistry. Engineering students will also find the set a valuable reference tool.