The main theme of this work can be divided into three categories, which can be summarized as follows: First, we give some definitions of impulsive differential equations with or without delays with some illustrative examples and some real life applications. Second, we give the explicit forms of the solutions of the boundary value problems (periodic and nonperiodic) which consist of the first order linear ordinary differential equations with non-constant coefficients together with finite impulsive conditions and boundary condition (periodic and nonperiodic). Third, we transform the boundary value problems (periodic and nonperiodic) which consists of the first order nonlinear ordinary differential equations together with finite impulsive conditions and boundary condition (periodic and nonperiodic) into equivalent integral equations. Also the existence of the solutions for the above periodic boundary value problems are discussed.