It is an excellent overview of the theory of relations between Riemann surfaces and their models - complex algebraic curves in complex projective spaces. To sum up, this book helps to learn algebraic geometry in a short time, its concrete style is enjoyable for students and reveals the beauty of mathematics."

From the reviews of the first printing, published as volume 23 of the Encyclopaedia of Mathematical Sciences:
"This volume... consists of two papers. The first, written by V.V.Shokurov, is devoted to the theory of Riemann surfaces and algebraic curves. It is an excellent overview of the theory of relations between Riemann surfaces and their models - complex algebraic curves in complex projective spaces. ... The second paper, written by V.I.Danilov, discusses algebraic varieties and schemes. ...
I can recommend the book as a very good introduction to the basic algebraic geometry."
European Mathematical Society Newsletter, 1996

"... To sum up, this book helps to learn algebraic geometry in a short time, its concrete style is enjoyable for students and reveals the beauty of mathematics."
Acta Scientiarum Mathematicarum, 1994