"Well-written and comprehensive introduction to Riemann surfaces and complex algebraic curves. Introduces sheaves and cohomology and proves Riemann-Roch."

"Really nice small book. This is a first abstract attempt to general algebraic geometry as introduces Sheaf theory and cohomology on varieties (not schemes yet!) and proves Riemann-Roch on an algebraic setting. Has lots of real exercises and problems (done in French universities) to work on."

"THE BOOK ON CLASSICAL ALGEBRAIC GEOMETRY. IF YOU REALLY WANT TO KNOW AND UNDERSTAND WHAT YOU ARE REALLY DOING IN ABSTRACT ALGEBRAIC GEOMETRY (i.e. Hartshorne and beyond) YOU SHOULD MASTER THIS TEXT FOR THE CLASSICAL APPROACH TO GEOMETRY BEFORE GETTING SUNK IN PURELY ALGEBRAIC ABSTRACTIONS WITHOUT MOTIVATION. Besides, it includes solutions to most problems along with many examples."

"Great new introductory book for complex geometry! It mixes differential and algebraic complex geometry with a focus on the latter. Very useful as an introduction to Hodge theory and more advanced texts like Voisin and Griffiths-Harris."

"THE introductory book on complex algebraic geometry. Indispensable to connect every approach together and as background reading for more advanced treatments like Griffiths/Harris."

"This book intends to introduce algebraic geometry through lots of (mostly classical) examples so in this sense is a good companion to more formal treatments. Nevertheless many results are not proved and it doesn't fit together as nicely as other titles. Fundamental to look up some nice examples or exercises though!"

"Wonderful book! very clear and complete. Instead on relying so much on commutative algebra as the previous one, Shafarevich develops a bit more classic approach. Very complete but (Russian!) exercises are kind of hard. Excellent as a companion to Hulek's. It's a pity it almost doesn't deal with Riemann-Roch."

"Vol. 2 of the previous title. This should be your first encounter with Schemes because Shafarevich guides you from the motivations and insights to really understand why things are done the way they are in more advanced texts. The other half of the book deals with an introduction to complex geometry (but still no Riemann-Roch)."

"THE BOOK for advanced classical algebraic geometry! Dolgachev develops lots of interesting classical topics with modern language. A true gem for any advanced lover of geometry."