Essential Advanced Physics is a series comprising four parts: Classical Mechanics, Classical Electrodynamics, Quantum Mechanics and Statistical Mechanics. Each part consists of two volumes, Lecture notes and Problems with solutions, further supplemented by an additional collection of test problems and solutions available to qualifying university instructors. This volume, Classical Mechanics: Lecture notes, is intended to be the basis for a one-semester graduate-level course on classical mechanics and dynamics, including the mechanics of continua, in particular deformations, elasticity, waves, and fluid dynamics.