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As mentioned in the title, i want to get started with number theory and I am searching for a book fitting my purposes. Ive just finished Calculus 1. I'd be glad if you could recommend a book written in English or German. Thank you in advance.

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    There are so many good books at all levels. But I'd seriously recommend studying a bit of abstract algebra first, before diving in to number theory. There are treatments that do not assume algebra, but honestly it's not a great way to do it, unless you want a very superficial treatment. – Gregory Grant Jul 06 '15 at 20:58
  • @GregoryGrant Thank you for the advice. Can you recommend a book for abstract algebra considering I want to get involved in Number Theory? –  Jul 06 '15 at 21:12
  • I haven't kept up with elementary abstract algebra books, but I know there are many of them. You just need the basics, groups, rings, fields, finite fields, usually the first three or four chapters. – Gregory Grant Jul 06 '15 at 22:31
  • @GregoryGrant I guess I'll have to annoy you with another question, after learning about all the basics of abstract algebra is there a book you can recommend which is not too hard but not that easy either because Silverman's Introduction to Number Theory seems kind of unchallenging. –  Jul 07 '15 at 08:40
  • Well, I used this book as an undergraduate: http://www.amazon.com/Introduction-Number-Theory-William-Adams/dp/0134912829/ref=sr_1_2?s=books&ie=UTF8&qid=1436263652&sr=1-2&keywords=number+theory+adams Then after learning algebra I used this book (when I was 2nd year graduate student): http://www.amazon.com/Number-Fields-Universitext-Daniel-Marcus/dp/0387902791/ref=sr_1_1?s=books&ie=UTF8&qid=1436263702&sr=1-1&keywords=number+theory+marcus – Gregory Grant Jul 07 '15 at 10:10
  • Then as a 3rd years graduate student we used this booK: http://www.amazon.com/Algebraic-Cambridge-Studies-Advanced-Mathematics/dp/0521438349/ref=sr_1_1?s=books&ie=UTF8&qid=1436263785&sr=1-1&keywords=number+theory+frohlich And finally as a 5th year graduate student we used this book: http://www.amazon.com/Algebraic-Number-Theory-William-Cassels/dp/0950273422/ref=sr_1_2?s=books&ie=UTF8&qid=1436263861&sr=1-2&keywords=number+theory+frohlich+cassels – Gregory Grant Jul 07 '15 at 10:11
  • @GregoryGrant Thank you. I've just ordered the Adam's "Introduction to Number Theory" and I'll be learning some Modern Algebra while waiting for it :) –  Jul 07 '15 at 10:29
  • I liked Adams, it's a pretty basic treatment, but I guess anybody interested in higher level number theory should read the down-to-earth treatment first. – Gregory Grant Jul 07 '15 at 10:45
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    Does this answer your question? Good Number Theory books to start with? –  Feb 01 '21 at 19:15

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I highly recommend Joseph H. Silverman's A Friendly Introduction to Number Theory. I used it last year in an introductory number theory course and had an amazing experience. It nicely balances mathematical rigor with a conversational and easy-to-follow style, covers a wide range of topics, and is full of well-crafted examples and exercises that will develop your number theoretic problem-solving chops. You will not need any prior knowledge beyond Calculus 1 (and even that will only come up when you study elliptic curves), and the book takes care to fill in any potential gaps in knowledge. The first six chapters are available for free on the website I linked.

hexaflexagonal
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    Thank you, I will consider buying this book. –  Jul 06 '15 at 21:09
  • I didn't know Silverman wrote an elementary number theory book. But I know he writes really well, and he has a keen perspective, so I have no doubt that it is good. – Gregory Grant Jul 06 '15 at 22:30
  • I read some of the reviews of this book and it looks like it's not really intended for math majors. So though it may be a great book for the intended audience, the OP may be looking for something a bit more rigorous. – Gregory Grant Jul 07 '15 at 13:19