This third edition closely follows the fifth German edition. In particular, it now contains an enlarged presentation of the "tippe top" and a new section on the use of Riemannian geometry in mechanics. As before, the book contains numerous problems with complete solutions, and some practical examples.This will be appreciated in particular by students using the text to accompnay lectures on mechanics. The main features of the book remain unchanged: the coverage extends from elementary Newtonian mechanics, Lagrangian as well as canonical Hamilton-Jacobian mechanics, the mechanics of rigid bodies, special relativity, and the geometric aspects of mechanics to the discussion of deterministic chaos and a short introduction to continuous systems. The book ends with some historical remarks on important pioneers in mechanics.