This book gives a thorough and entirely self-contained, in-depth introduction to a specific approach to group theory, in a large sense of that word. The focus lie on the relationships which a group may have with other groups, via -universal properties-, a view on that group -from the outside-. This method of categorical algebra, is actually not limited to the study of groups alone, but applies equally well to other similar categories of algebraic objects.

By introducing protomodular categories and Mal'tsev categories, which form a larger class, the structural properties of the...