Title: Properties of Low Dimensional Dynamical Systems in the Large Author: C. Sim\'o Dept. de Matem\`atica Aplicada i An\`alisi, Univ. de Barcelona, Gran Via 585, 08007 Barcelonar, Spain. E-mail: carles@maia.ub.es Lectures given at the Wolfgang Pauli Institute Vienna, 070108 to 070112 The objective of these lectures is to introduce to the study of systems having a moderate number of dimensions and/or parameters. The main goal is the study in large parts of the phase space times the parameter space. First several simple paradigmatic models will be presented and analyzed by means of analytic and numerical tools. Then details about the tools will be given concerning: a) Long-term simulations of discrete systems and numerical integration of differential equations. b) Dynamical indicators such as Lyapunov exponents, rotation numbers, Frequency Analysis. c) Computation, continuation with respect to parameters, detection and analysis of bifurcations for fixed points, periodic solutions, invariant curves, invariant tori. d) Same items for invariant manifolds of normally hyperbolic objects. Computation of homoclinic and heteroclinic orbits. Dynamical consequences and applications. e) Towards global study of the dynamics: Codimension 1 manifolds. Sketch of some computer assisted rigorous proofs.