This two-part EMS volume provides a succinct summary of complex algebraic geometry, coupled with a lucid introduction to the recent work on the interactions between the classical area of the geometry of complex algebraic curves and their Jacobian varieties. An excellent companion to the older classics on the subject.

From the reviews: "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

From the reviews: "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

This two-part EMS volume provides a succinct summary of complex algebraic geometry, coupled with a lucid introduction to the recent work on the interactions between the classical area of the geometry of complex algebraic curves and their Jacobian varieties. An excellent companion to the older classics on the subject.