We present, in these lectures, the basic theorems of the theory of global stability of dynamical systems, among them Smale's $\Omega$-stability theorem, and the rationality of the $\zeta$ function of an Axiom $A$ diffeomorphisrn. The reader will find here, among other things, the basic tools for the study of hyperbolic invariant sets : filtration theory, the stable manifold theorem, stability of hyperbolic sets, local product structure and existence of Markov partitions.