This textbook presents an up to date  perspective on the fundamental elements of theoretical physics. It encompasses analytical mechanics, thermodynamics and statistical physics, special and general relativity, and non-relativistic quantum theory, thoroughly developing the necessary mathematical methods beyond standard calculus while striving to be as clear, explicit, and direct as possible. The exposition of the theory, both in the classical and quantum parts, is expanded and reworked compared to the first edition. In parallel with the formalism, which is explained in full detail,...