Physical theories, fundamental constants and the role of Mathematics -- Analytical Mechanics -- Dirac’s delta -- Green’s functions for Electromagnetism -- Equilibrium Thermodynamics -- Classical Statistical Mechanics -- Relativity -- Particles and waves from classical to Quantum Mechanics -- Schroedinger equation -- Elementary solutions in one dimension -- Postulates and formulations of Quantum Mechanics -- Separation of variables -- Angular momentum–Hydrogen atom -- Discrete models -- Fano resonances and Green’s functions -- Spin -- Quantum statistics and many-body phenomena -- Non-equilibrium phenomena and quantum transport -- Berry Phase -- Quantum Statistical Mechanics -- Entanglement, EPR paradox. Teleportation -- Perturbation theory -- Variational method in Quantum Mechanics -- Recursion methods -- Mathematical appendices: Tensors - Hermite and Laguerre Polynomials.

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, several more experimental phenomena and techniques are included and discussed. Throughout, the emphasis is on the physical meaning of the theory, that is, the precise way in which the necessary experimental verification occurs or might occur in the future. With its comprehensive approach, rigorous mathematical treatments, and clear, physically oriented explanations of principles and experiments, this textbook is an essential resource for advanced undergraduate and graduate students of physics, as well as a valuable reference for researchers.