When I read the title of this book, I expected it to be a comprehensive treatment of the topic. After reading the first few pages, I found out that this was not what the author had in mind. Actually, the scope of the book is limited to the theory of Volterra-type integral, integro-differential, and delay integral equations, with a special emphasis on the question of the long-term behavior of their solutions, for example, the various concepts of stability that are available in the literature.

This topic is covered in a very comprehensive way. The main tool is the theory of Lyapunov functionals, a classical method whose value sometimes seems to be underestimated. Throughout the book, the author emphasizes the fact that Volterra equations are more general than the more commonly used differential equations. To illustrate this fact, the results obtained in the book for Volterra equations are often compared to similar results for differential equations. The statements derived in the book are likely to have a substantial influence on the theory of stability of numerical methods for Volterra equations, but the author has decided not to elaborate on this matter, thus keeping a purely theoretical focus.

The book provides an excellent survey of the state of the art of a rather narrow area of pure mathematics (certainly much narrower than the title indicates). The results are also of potentially high value for those working on the theoretical foundations of computational mathematics. The standard of typesetting is good, but a better index would have enhanced the book.