My favorite intros to algebraic geometry are these: Igor R. Shafarevich, Basic Algebraic Geometry, two volumes, third edition, Springer, 2013. Phillip Griffit

My favorite intros to algebraic geometry are these: Igor R. Shafarevich, Basic Algebraic Geometry, two volumes, third edition, Springer, 2013. Phillip Griffiths and Joseph Harris, Principles of Algebraic Geometry, 1994. (Especially nice if you like complex analysis, differential geometry and de Rham theory.) David Eisenbud and Joseph Harris, The Geometry of Schemes, Springer, 2010. Currently at https://www.maths.ed.ac.uk/~v1ranick/papers/eisenbudharris.pdf https://www.maths.ed.ac.uk/~v1ranick/papers/eisenbudharris.p... But whenever I want to learn some new field of math I start with Wikipedia. This is a pretty good overview: https://en.wikipedia.org/wiki/Algebraic_geometry https://en.wikipedia.org/wiki/Algebraic_geometry