This book presents a comprehensive study of abstract linear integral equations, particularly evolutionary integral equations, and their applications in mathematical physics. It covers both scalar and nonscalar types of equations, including Volterra equations and parabolic equations. The book is structured into chapters that discuss the theory, applications, and related concepts in detail. The main focus is on the linear theory, which has reached a state of maturity, and it aims to provide a coherent exposition of the current state of the art. The text includes a detailed discussion of resolvents, analytic resolvents, and their properties, as well as the theory of parabolic equations and their applications in viscoelasticity, heat conduction, and electrodynamics with memory. The book also addresses the concept of subordination and its implications for the solutions of integral equations. It includes a variety of model problems from mathematical physics, such as viscoelasticity, heat conduction in materials with memory, and electrodynamics with memory. The text is written for researchers and students in the fields of mathematics and physics, and it provides a thorough treatment of the subject matter, including detailed proofs and references to relevant literature. The book is intended to serve as a reference for those working in the area of abstract Volterra equations and their applications.This book presents a comprehensive study of abstract linear integral equations, particularly evolutionary integral equations, and their applications in mathematical physics. It covers both scalar and nonscalar types of equations, including Volterra equations and parabolic equations. The book is structured into chapters that discuss the theory, applications, and related concepts in detail. The main focus is on the linear theory, which has reached a state of maturity, and it aims to provide a coherent exposition of the current state of the art. The text includes a detailed discussion of resolvents, analytic resolvents, and their properties, as well as the theory of parabolic equations and their applications in viscoelasticity, heat conduction, and electrodynamics with memory. The book also addresses the concept of subordination and its implications for the solutions of integral equations. It includes a variety of model problems from mathematical physics, such as viscoelasticity, heat conduction in materials with memory, and electrodynamics with memory. The text is written for researchers and students in the fields of mathematics and physics, and it provides a thorough treatment of the subject matter, including detailed proofs and references to relevant literature. The book is intended to serve as a reference for those working in the area of abstract Volterra equations and their applications.