In 1995, Andrew Wiles completed a proof of Fermat's Last Theorem. Although this was certainly a great mathematical feat, one shouldn't dismiss earlier attempts made by mathematicians and clever amateurs to solve the problem. In this book, aimed at amateurs curious about the history of the subject, the author restricts his attention exclusively to elementary methods that have produced rich results.
This is a good book for professional mathematicians. The material is presented in a way that passes all tests for strictness (and mathematicians are fond of that), but not the tests for making ideas clear by way of examples (when that's possible). Some chapters are very tough, I dare say they give a hard time even to specialists in number theory. So the biggest mistake of this book is the "for amateurs" in the title: that's totally misleading.