I don't like reviews that sound like the electoral returns of a communist dictatorship, i.e. no opposition, so when I come across a particularly good book, I sometimes look hard for something negative. I found two things wrong with Pinter's book.<br><br>* First, it will not enlighten me to the mysteries of living the good life, nor will it make me rich.<br><br>* Second, the author uses too many exclamation marks.<br><br>Try as I might, I can't really find anything else wrong with this excellent and thorough introduction to abstract algebra.<br><br>The book is rigorous; it presents all the important theorems with accompanying proofs and defines its terms clearly. Each short chapter defines terms and proves the basic theorems concerning one topic, after which it ends with exercises gathered together under topical headings. It is vital to read and understand the exercises by the way, and to work out many of them. They contain important ideas and concepts needed to understand later chapters.<br><br>For instance, a series of exercise develop the idea that a permutation is more than a reordering of a finite number of objects. A permutation is a reordering of any number of things, including an infinite or even uncountable number of things. For example the function f(x)=2x+1 is a permutation from R to R because it takes each real number and sends it to a different unique real number (f(1.5)=4) while conversely each real number has a unique inverse under that function (i.e. the inverse of 4 under our function f is 1.5). This makes f a permutation.<br><br>Pinter could perhaps have developed some topics further, for instance it would be nice to have more about the classification of permutations, but he does cover their basics and devotes some space to the major classifications, such as the symmetric groups and the cyclic groups, but without emphasizing the fact that classifying groups is a major area of study in its own right.<br><br>Vincent Poirier, Tokyo