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Rating: 
Summary: High-level math, as expected from Hormander
Review: I started to learn several complex variables a few weeks ago, and I noticed the absolute lack of textbooks on the subject. Probably the book that comes more naturally as an extension of undergraduate complex analysis is Gunning and Rossi, but this title is out-of-print (even finding a used copy is nearly impossible. Believe me, I've tried hard). So, we have Hormander's book. Lars Hormander is known for writing high-level math texts (both in quality and difficulty), as seen in his famous 4-volume series about PDE's, and this book is no exception. His point of view is more related to his area of research (PDE's, again), and his demands for prerequisites are higher than GR (basics from Lebesgue integration, differential forms, algebra and point-set topology are more than welcome), but this book is a masterpiece of mathematical craftsmanship. The methods here developed are often unique, and the author presents the subject in a fully rigorous way. Along with the fact that it is one of the very few books on several complex variables still in print, this is a very valuable text, set in a high standard of excellence. My only complaint is the obscenely high price for a book so important. Several complex variables are an indispensable background for complex manifolds and algebraic geometry, and several important topics in theoretical physics (string theory, twistor theory, conformal field theory), and it's a shame that books like GR go out-of-print without any others for substituting them. Hormander's book doesn't go much deep in these directions, but you won't find any other book in print on the subject with such a high quality.
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