The "Theory of Groups of Finite Order" by Burnside was first published in 1897 and a second edition in 1911; the Dover Phoenix edition is a reprint of the second edition. The book can be considered as a milestone in the theory of groups. In all prior books (with the exception of Weber's "Lehrbuch der Algebra"), the term group meant "permutation group". Burnside book intended to popularize the notion of an abstract group with the publication of this book.

Groups are defined in the second chapter, after an initial chapter on permutations. The third and fourth chapter discuss the basics of groups, including subgroups, normal subgroups, factor groups, commutators and the derived subgroup. The fifth chapter introduces the composition series of a group, and the sixth chapter discusses the automorphism group of a group. Abelian groups are discussed in chapter seven, and p-groups in chapter eight. The Sylow theorems are discussed in chapter nine. Later chapters are devoted to permutation groups, representations of groups by permutation groups, linear groups, representation theory, and even some infinite groups.

Burnside's book is still very readable, although some of terminology has changes since then. An attractive feature of the book is that it contains many more examples than one typically finds in more recent books on group theory. The exposition is very clear, so that even non-specialists can profit quite a bit. It is rather remarkable how much knowledge was already available one hundred years ago.

The book is not just interesting for historical reasons, but it provides much more examples than more recent books. Overall, I can highly recommend this classic masterpiece.