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For context, I am a undergraduate majoring in math. I've taken two semesters of algebra (though I am still a bit shaky on Galois theory). I just finshed a course in elementary number theory which used George Andrew's text.

This introductory course in number theory has been my favorite math class and I hope to learn a bit of algebraic number theory this summer to hopefully do an independent study/senior thesis in the next school year.

What are the best gentle introductory algebraic number theory texts that give an overview of the subject?

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  • $\begingroup$ For gentle introduction, I'd look at Alaca and Williams, "Introduction to Algebraic Number Theory." It is also relatively inexpensive. But it doesn't have so much of an "overview" of the subject. Also look at Milne's online notes. $\endgroup$ – John M Jun 4 '14 at 23:51
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Not sure if it's gentle, but A Classical Introduction to Modern Number Theory by Ireland and Rosen appears to have received excellent reviews on Amazon.com, so perhaps that might be worth a look.

Alternatively, I found another one by William Stein's Elementary Number Theory: Primes, Congruences, and Secrets.

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  • $\begingroup$ I think Ireland & Rosen is excellent but maybe not so gentle. $\endgroup$ – Charles Jun 4 '14 at 3:52

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