Complex analysis book for Algebraic Geometers I know that there exist many questions on this site on complex analysis books but my question is more specific than that. I am looking for recommendations for a concise complex analysis book but with a view towards algebraic geometry/ complex manifolds. I have studied smooth manifold theory before and it would be interesting to see it combined with complex analysis in the complex setting (all manifolds that I'd studied before were real manifolds). Any recommendations for such a book?

From Holomorphic Functions to Complex Manifolds by Klaus Fritzsche and Hans Grauert is a great introduction to complex manifolds with also a very nice course on several complex analysis. It's not really oriented on algebraic geometry, though.
Hans Grauert is one of the founder of the complex geometry.
