This book presents recent methods of study on the asymptotic behavior of solutions of abstract differential equations such as stability, exponential dichotomy, periodicity, almost periodicity, and almost automorphy of solutions. The chosen methods are described in a way that is suitable to those who have some experience with ordinary differential equations. The book is intended for graduate students and researchers in the related areas. Contents: Stability and Exponential Dichotomy; Almost Periodic Solutions; Almost Automorphic Solutions; Nonlinear Equations.