Title: Studies in Dynamics: From local to Global aspects Author: Carles Sim\'o Dept. Matem\`atica Aplicada i An\`alisi, Univ. de Barcelona, Gran Via 585, 08007 Barcelona, Spain E-mail: carles@maia.ub.es Lecture given at the opening of the 2007-2008 course in the Societat Catalana de Matematiques, Barcelona 071019 Abstract We are interested in problems of Dynamics, either in discrete or continuous systems, driven by ODE or PDE. Applications can be found in all scientific and technical domains. As it happens in many domains of Mathematics most of the results in Dynamics follow in one of these classes: either they give a very precise description of some phenomena but tehy have a very local character, or they give a global information but it is very rough. There are results on existence of some phenomena without a constructive approach and without making precise a realistic estimate of the domain of validity. The goal of this lecture is to show that one can understand many of the global characteristics of simple mathematical models by using different ``submodels'' which allow to understand qualitatively and quantitatively the most relevant aspects of the dynamics.