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I am looking for something that treats singularities on algebraic surfaces and curves over $\mathbb{C}$, starting from the very basics but not stopping there.

I checked out Miles Reid his lectures on algebraic surfaces and they seem promising (especially the exercises). Also Harris - algebraic geometry a first course seems nice. However, the first gets very technical quickly while the second book's treatment of singularities is pretty short.

Is there also something that treats loads and loads of examples, furnishing a good intuition about the subject?

Thanks!

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"Basic Algebraic Geometry 1: Varieties in Projective Space" by Igor R. Shafarevich is a nice text that is quite elementary. Surface singularities are studied on page 264, it may be what you are looking for.

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"Lectures on Resolution of Singularities" (Annals of Mathematics Studies, 166) by Kollár also comes to mind. This probably goes a bit further than you need, but the first two chapters (about two-thirds of the length of the book) deal with curve and surface singularities in detail.

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You might enjoy "Introduction to Singularities and Deformations" by Greuel, Lossen, and Shustin. The flavour is complex analytic, but many examples and techniques overlap with the algebraic category. (And it is available on SpringerLink, so it should be easy to find a copy online.)

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This site looks very interesting to learn about algebraic surfaces.

http://touch-geometry.karazin.ua/list

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