This book discusses exponential integrators, which are numerical methods. We encountered this method in many fields such as Plasma Physics, Combustion and Fluid Mechanics. The book includes four chapters: Chapter 1 illustrates what are exponential integrators. Chapter 2 illustrates what are stiffness problems. Chapter 3 discusses the time integrators of semi linear stiff problems. Chapter 4 presents a review of time discretization of semi linear parabolic problems.