This text gives an introduction into the ideas of dynamical systems. It is divided into two parts which can be treated in either order: the first part treats the aspects coming from systems of nonlinear ordinary differential equations, and the second part is comprised of those aspects dealing with iteration of a function. Its main emphasis is on the types of behavior which nonlinear systems of differential equations can exhibit. The text assumes that students have taken courses on calculus covering both a single variable and multivariables, a course on linear algebra, and an introductory course on differential equations.