The limitations of classical physics -- Elements of vector analysis -- The classical harmonic oscillator -- Angular momentum and energy in classical physics -- The special theory of relativity -- Introduction to mathematical probability and its applications in physics -- Elements of statistical mechanics -- Classical wave motion -- Introduction to quantum mechanics -- The basic assumptions of quantum mechanics -- Mathematical properties of operators and state functions -- The central-field problem in quantum mechanics -- Noted on the quantum-mechanical treatment of typical multiparticle system -- Elements of perturbation theory -- Introduction to the Dirac equation.