Hyperbolicity in geometry: The concept of a contracting geodesic in a metric space is introduced. Examples are geodesics in the hyperbolic plane. We discuss more general examples, with applications to rigidiy in mind.

Hyperbolicity in dynamics: The concept of a hyperbolic dynamical system is introduced. Examples are the geodesic flow on a closed hyperbolic surface. We weaken the concept and discuss geometric examples which relate to hyperbolicity in metric spaces as in Lecture 1, with applications to rigidity in mind.

Hyperbolicity in groups: The notion of a hyperbolic group is introduced. Examples are the fundamental group of a closed surface of higher genus. We discuss more general hyperbolic features of groups inherited by interesting actions o f the group on spaces with hyperbolic features relating to lectures 1 and 2.