We give a brief introduction to the theory of nonlinear hyperbolic systems of conservation laws. The talk is intended for beginning graduate students. We begin with the basic notion of hyperbolicity, and briefly discuss first order constant coefficient linear hyperbolic systems. We then discuss scalar nonlinear conservation laws in order to demonstrate simple waves and shock formation. We derive the Rankine-Hugoniot condtions on jump discontinuities and demonstrate the need for entropy conditions. As time permits, we will discuss simple waves and shock waves for systems.