Abstract: Many natural problems can be described as an abstract Cauchy problem (ACP). This includes initial value or initial- boundary value problems arising from the partial differential equations (PDEs). These problems find applications in physics, mechanics, engineering, control theory, etc. They can be put as an (ACP) by considering the associated differential operator in the space variables as operators in some function space. This leads to defining the domain of the operator and considering the boundary conditions into the domain of the operator. The aim of these courses is to prepare a simple and independent presentation of the theory of semi-groups of bounded linear operators and its application in PDEs. After the introduction, we will find, in chapter 1, some preliminary results: definitions, lemmas and theorems that we will use throughout these courses. Then, in chapter 02, we introduce the theory of one-parameter semigroups of bounded linear operators. Chapter 03 is concerned with study in detail of the (ACP). First we will study the homogeneous problem and the nonhomogeneous problem, and on the occasion we give some illustrative applications to PDEs. Then we will focus on the regularity and the asymptotic behavior of the solutions.