Evolutionary processes with memory exist extensively in the world. The presence of memory poses significant challenges for understanding, analyzing, predicting, and synthesizing these processes. This book studies properties of evolutionary processes with memory by introducing a pair of bounded linear operators, known as resolvent family, to represent solutions. The generation issue of resolvent family is also discussed. Additionally, this book presents the dual problem of evolutionary processes, including solvability issues related to semi-linear equations and linear equations with time-varying memory. Finally, it explores invariant subspace and spectral issues related to evolutionary process with memory. This book is written for students of mathematics and engineering, engineers in control theory, and mathematical researchers. The scholars and readers who are interested in mathematical analysis and its applications will find innovative issues and theories.