This book provides an introduction to the major mathematical structures used in physics today. Topics covered include group theory, Lie algebras, topology, Hilbert space and differential geometry. Important theories of physics such as classical and quantum mechanics, thermodynamics, and special and general relativity are also developed in detail. The book is suitable as a textbook for advanced undergraduate and beginning graduate students. It includes numerous exercises and worked examples, to test the readers understanding of the various concepts, as well as extending the themes covered in the main text.