Group Theory is a vast subject and， in this Introduction （as well as in the earlier editions）， I have tried to select important and representative theorems and to organize them in a coherent way. Proofs must be clear， and examples should illustrate theorems and also explain the presence of restrictive hypotheses. I also believe that some history should be given so that one can understand the origin of problems and the context in which the subject developed.
Just as each of the earlier editions differs from the previous one in a significant way， the present （fourth） edition is genuinely different from the third. Indeed， this is already apparent in the Table of Contents. The book now begins with the unique factorization of permutations into disjoint cycles and the parity of permutations； only then is the idea of group introduced. This is consistent with the history of Group Theory， for these first results on permutations can be found in an 1815 paper by Cauchy， whereas groups of permutations were not introduced until 1831 （by Galois）， But even if history were otherwise， I feel that it is usually good pedagogy to introduce a general notion only after becoming comfortable with an important special case. I have also added several new sections， and I have subtracted the chapter on Homological Algebra（although the section on Hom functors and character groups has been retained）and the section on Grothendieck groups.
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