Abstract
Our main goal is to study Ramsey Ergodic Theory, wich relates the areas of Dynamical Systems and Ramsey Theory. In this project our main tool will be the Stone-Cech compactification of a countable discrete semigroup, consisting of the set of ultrafilters over such semigroup. With this it is possible, for example, to generalize the concept of limit in a compact Hausdorff space, extending t…