Basic concepts of analytical mechanics. Generalized coordinates. Variational principles of mechanics. Hamilton’s principle of least action. Euler-Lagrange equations. Lagrangian for a system of particles. Conservation laws. Energy, momentum, angular momentum. Mechanical similarity and virial theorem. Systems with one and two degrees of freedom. Phase flow. Motion in a central field. Kepler’s problem. Elastic collisions. Rutherford’s formula. Small oscillations. Normal coordinates. A chain of coupled oscillators. Rigid body motion. The Euler angles. The Cayley-Klein parameters. Inertia tensor. The Euler top. The Lagrange top.