This paper is the first part of a two-part survey reviewing somebasic concepts and methods of the modern theory of dynamical systems.The survey is introduced by a preliminary discussion of the relevanceof nonlinear dynamics and chaos for economics. We then discuss thedynamic behavior of nonlinear systems of difference and differentialequations such as those commonly employed in the analysis ofeconomically motivated models. Part I of the survey focuses on thegeometrical properties of orbits. In particular, we discuss thenotion of attractor and the different types of attractors generatedby discrete- and continuous-time dynamical systems, such as fixed andperiodic points, limit cycles, quasiperiodic and chaotic attractors.The notions of (noninteger) fractal dimension and Lyapunovcharacteristic exponent also are explained, as well as the mainroutes to chaos.