The approach to classical mechanics adopted in this text includes recent developments in nonlinear dynamical systems, and the concepts necessary to formulate and understand chaotic behavior are presented. Besides the conventional topics (such as oscillators, the Kepler problem, spinning tops and the two centres problem) studied in the frame of Newtonian, Lagrangian, and Hamiltonian mechanics, nonintegrable systems (the Henon-Heiles system, the Coulomb force and the homogeneous magnetic field, the restricted three-body problem) are also discussed. The question of the integrability (of planetary motion, for example) leads finally to the KAM-theorem. This work is the result of lectures on Classical Mechanics as the first part of a basic course in Theoretical Physics. These lectures were given by the author to undergraduate students in their second year at the Johannes Kepler University Linz, Austria. The work is also addressed to lecturers in this field and to physicists who want to obtain a new perspective on classical mechanics.