ABSTRACT: The goal of these four lectures is to learn how systems governed by known equations of motion, with no randomness, can still display an unpredictable temporal evolution. This seemingly contradictory phenomenon, known as deterministic chaos, was first discovered in Astronomy and Meteorology but is now known to appear in virtually all scientific disciplines. The complicated chaotic dynamics appears already in very simple (yet non-linear) equations, which we will study analytically and through simple computer simulations. Our excursion to understand chaos will lead us to some fundamental concepts in the mathematical theory of dynamical systems, such as attractors, bifurcations, invariant measure, Lyapunov exponents, and self-similarity.