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Customer Reviews:
Crystal clear
By Smeets Arne - February 23, 2010Samuel's book is a classic. It is a bit "antique", certainly not the most modern introduction to algebraic number theory. The topics covered in the book are algebraic and integral extensions, Dedekind rings, ideal classes and Dirichlet's unit theorem, the splitting of primes in an extension field and some Galois theory for number fields. So the range of topics is quite small (and the book is short, ~100 pages).
And yet I love this book. It is crystal clear, well written and well structured; it is quite dense (especially the last chapter) and makes the beginning student of algebraic number theory think a lot, but without ever getting too heavy to digest. The list of problems is fantastic: there are many very concrete problems which sharpen your understanding of the material considerably. And last but not least, it is ridiculously cheap.
I recommend this to anyone who wants to learn the basic material about number fields. Without any hesitation.
beautifully written
By Narada "the wondering jew" - December 27, 2010(I have read this book in French, so can't comment on the translation). This is the best introduction to number theory, and the Dover price certainly can't be beat. The one problem with this book is that the perspective is very Bourbakist, and so the arguments do not tend to be constructive, so you might want your next book to be
Dense and hard to read
By Ben Kraft - April 6, 2013This book is fairly classic, but it's pretty dense and hard to read. The typesetting is also pretty bad. You're probably better off using one of the various good sets of online notes for algebraic number theory (J.S. Milne's, for example). If you want a book, though, this one will do, and it's nice and small.
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