This lecture introduces the fundamental concepts of the Hyperbolic Theory of Dynamical Systems, providing an accessible entry point for graduate students. We shall explore the core ideas of hyperbolicity, including stable and unstable manifolds, uniform expansion and contraction, and the study of hyperbolic systems. Through intuitive examples, such as Anosov diffeomorphisms, the Smale horseshoe and Plynkin attractors, we shall illustrate how hyperbolicity leads to chaotic yet structured behaviour. Emphasis will be placed on geometric intuition and generic properties of Dynamical Systems. No prior expertise in dynamics is assumed, hoping that this lecture will serve as a friendly introduction to a cornerstone of modern dynamical systems.