© 1992

Riemann Surfaces


Part of the Graduate Texts in Mathematics book series (GTM, volume 71)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Hershel M. Farkas, Irwin Kra
    Pages 1-8
  3. Hershel M. Farkas, Irwin Kra
    Pages 9-31
  4. Hershel M. Farkas, Irwin Kra
    Pages 32-53
  5. Hershel M. Farkas, Irwin Kra
    Pages 54-165
  6. Hershel M. Farkas, Irwin Kra
    Pages 166-256
  7. Hershel M. Farkas, Irwin Kra
    Pages 257-297
  8. Hershel M. Farkas, Irwin Kra
    Pages 298-320
  9. Hershel M. Farkas, Irwin Kra
    Pages 321-355
  10. Back Matter
    Pages 356-366

About this book


It is gratifying to learn that there is new life in an old field that has been at the center of one's existence for over a quarter of a century. It is particularly pleasing that the subject of Riemann surfaces has attracted the attention of a new generation of mathematicians from (newly) adjacent fields (for example, those interested in hyperbolic manifolds and iterations of rational maps) and young physicists who have been convinced (certainly not by mathematicians) that compact Riemann surfaces may play an important role in their (string) universe. We hope that non-mathematicians as well as mathematicians (working in nearby areas to the central topic of this book) will also learn part of this subject for the sheer beauty and elegance of the material (work of Weierstrass, Jacobi, Riemann, Hilbert, Weyl) and as healthy exposure to the way (some) mathematicians write about mathematics. We had intended a more comprehensive revision, including a fuller treatment of moduli problems and theta functions. Pressure of other commitments would have substantially delayed (by years) the appearance of the book we wanted to produce. We have chosen instead to make a few modest additions and to correct a number of errors. We are grateful to the readers who pointed out some of our mistakes in the first edition; the responsibility for the remaining mistakes carried over from the first edition and for any new ones introduced into the second edition remains with the authors. June 1991 Jerusalem H. M.


Hilbert space Meromorphic function Riemann surfaces Riemann-Roch theorem Riemannsche Fläche Surfaces ring theory

Authors and affiliations

  1. 1.Department of MathematicsHebrew UniversityJerusalemIsrael
  2. 2.Department of MathematicsState University of New YorkStony BrookUSA

Bibliographic information

  • Book Title Riemann Surfaces
  • Authors Hershel M. Farkas
    Irwin Kra
  • Series Title Graduate Texts in Mathematics
  • DOI
  • Copyright Information Springer-Verlag New York, Inc. 1992
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-97703-4
  • Softcover ISBN 978-1-4612-7391-2
  • eBook ISBN 978-1-4612-2034-3
  • Series ISSN 0072-5285
  • Edition Number 2
  • Number of Pages XVI, 366
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
    Topological Groups, Lie Groups
    Algebraic Geometry
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