I am currently an undergraduate mathematics student who is interested in studying more about complex/analytic geometry. However, most undergraduate modules (at least in my home university) do not cover the substantial background material required to understand the myriad theorems and lemmas in that area of mathematics i.e. several complex variables, complex manifolds, algebraic geometry, sheaves....
Hence, what texts can I use as introductory material to build up the necessary foundation. A friend recommended Atiyah and Macdonald as a precursor to the algebra required for Hartshorne's Algebraic Geometry. Are there any other recommendations (i.e. texts that might cover the topics listed above)?
P.S. I have completed the usual undergraduate courses in complex analysis, algebra and analysis.
I think the book Algebraic and Analytic Geometry by Neeman might be a good option. It is entirely focused on showing some connections between algebraic and analytic geometry, including GAGA.
I believe its target audience is around the end of an undergraduate programme, so shouldn't be intractable.