TITLE: Cantor Spectrum for quasi-periodic Schr\"odinger Operators AUTHOR: Joaquim Puig. Departament de Matem\`atica Aplicada i An\`alisi, Univ. de Barcelona, Gran Via 585, 08007 Barcelona, Spain. puig@maia.ub.es ABSTRACT: We present some results concerning the Cantor structure of the spectrum of quasi-periodic Schr\"odinger operators. These are obtained studying the dynamics of the corresponding eigenvalue equations, specially the notion of reducibility and Floquet theory. We will deal with the Almost Mathieu case, and the solution of the ``Ten Martini Problem'' for Diophantine frequencies, as well as other models.