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I am currently looking to study Algebraic Geometry. As I am totally new to the subject any reference for books to follow will be helpful, thanks in advance....

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    I found Brendan Hassett's book "Introduction to Algebraic Geometry" to be pretty easy to work with. It won't take you deep into schemes, or anything like that, but it gets through the basics pretty concretely, including elimination theory and projective geometry. – G Tony Jacobs May 19 '17 at 17:18
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    These (one and two) posts by Javier Álvarez are quite ... voluminous. And searching his answers, they are not the only ones. – pjs36 May 19 '17 at 17:25
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    You shoud precise more about your background and your objective as algebraic geometry is a pretty big subject... –  May 19 '17 at 20:16

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Cox, Little, O'Shea: Ideals, Varieties, and Algorithms. This is the standard book at the undergraduate level.

Wuestenfux
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    Standard book? First time i hear about this book ;) – Rüdiger May 19 '17 at 18:58
  • @Rüdiger, I'm not sure if it's standard but it's at least somewhat popular, especially if you want a computational approach focusing on Gröbner bases and Buchberger's algorithm. For a recent introductory algebraic geometry book that's open-access and well worth a look, see Beginning in Algebraic Geometry by Clader & Ross. – J W Jun 22 '25 at 07:35