In this book, we present the fundamental theory of abstract Evolution Equations by using the semigroup approach. More precisely, first we review the basic notions of Functional Analysis and Differential Analysis, secondly we study the theory of semigroups of bounded linear operators, and thirdly we consider Linear Evolution Equations and moreover we give existence results for Semilinear Evolution Equations of the form: du/dt= Au ] f(t; u); t 0; u(0) = u_0 where A is a linear operator that is the infinitesimal generator of a C_0-semigroup of bounded linear operators on a Banach space and f...