Introduction to Abstract Algebra

This textbook covers an introductory course in general algebra. The approach is elementary but rather abstract. One can trace the author's research interests to the border between algebra and category theory, which gives the textbook its unique flavour. The abstract approach is balanced by an abundance of illuminating examples and exercises, from the obvious up to difficult study projects. However, the book mostly avoids applications outside algebra and it also avoids some harder parts of the usual algebraic curricula, such as Galois theory. The book uses the traditional concept of groups first and rings next, while many properties are stated on the level of weaker structures such as semigroups and monoids. The contents are as follows. The first three chapters explain the fundamentals: numbers, functions and equivalences, staying on a concrete level. In the middle part, abstract groups and rings and fields, with the standard algebraic technology, are introduced. The final chapters include topics on factorization, modules, group actions and quasigroups.

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