This book is a comprehensive compilation covering most areas in mathematical and theoretical Physics. It provides a collection of problems together with their detailed solutions valuable to students & to researchers in the fields of Mathematics, Physics, engineering and other sciences. Each br>Chapter provides a short introduction with the relevant definitions and notations. The topics range in difficulty from elementary to advanced. Almost all problems are solved in detail and most of the problems are self-contained. Students can learn important principles and strategies required for problem solving. Important concepts and techniques are developed in the problems. More advanced problems together with their detailed solutions are collected, to meet the needs of graduate students and researchers. Problems included cover new fields in theoretical and mathematical Physics such as tensor product, lax representation, b?cklund transformation, soliton equations, Hilbert space theory, uncertainty relation, br>entanglement, spin systems, lie groups, Bose system, fermi systems differential forms, lie Algebra valued differential forms, metric tensor fields, hirota technique, painlev? test, bethe ansatz, yang?baxter relation, wavelets, gauge theory, differential Geometry, string theory, chaos, fractals, complexity, ergodic theory, etc. A number of soft.