Introduction: a brief history of the evolution of the science of motion; early notions of space, matter and motion; evolution of the language of mechanics: acceleration- Merton school of thought and Galileo; concept of inertia - Galileo and Descarte; momentum, force, mass and energy - Heugens, Newton and Leibniz; relational mechanics and the absolute - relative debate.
Universal gravitation and action-at-a-distance: gravitational and inertial mass and their equivalence; Mach's principle and origin of inertia; inertia as a manifestation of dynamic gravitational interaction.
Emergence of analytical mechanics; variational principles of mechanics; Lagrangian and Hamiltonian formulations; generalized coordinates and momenta; evolution of the concept of momentum; phase space; birth of statistical mechanics.
Matter waves in classical mechanics; optics-mechanics analogy; Hamilton-Jacobi theory; Hamilton - Schroedinger equation;
Frames of reference and principle of relativity; concept of space-time continuum; special theory of relativity; relativistic dynamics - concepts; mass energy equivalence; physical foundation of general theory of relativity; principle of equivalence and a metric theory of gravity; some relevant cosmological problems and open questions.
Quantum mechanics - conceptual foundations; Relation with classical mechanics.