Chapter I. Riemann surfaces: Basic definitions Chapter II. Functions and maps Chapter III. More examples of Riemann surfaces Chapter IV. Integration on Riemann surfaces Chapter V. Divisors and meromorphic functions Chapter VI. Algebraic curves and the Riemann-Roch theorem Chapter VII. Applications of Riemann-Roch Chapter VIII. Abel's Theorem Chapter IX. Sheaves and Čech cohomology Chapter X. Algebraic sheaves Chapter XI. Invertible sheaves, line bundles, and ˇH1

The author of this monograph argues that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play.