Lectures:  Exercises:  
Lecture 1, Tuesday, September 17, 2013 Definition of Riemann surfaces, first examples and properties. 
Exercises from Lecture 1 psfile , pdffile  
Lecture 2, Tuesday, September 24, 2013 Meromorphic functions, first properties of morhisms of Riemann surfaces. 
Exercises from Lecture 2 psfile , pdffile  
Lecture 3, Tuesday, October 1, 2013 Elementary properties of morhisms of Riemann surfaces. Homotopy of curves, fundamental group. 
Exercises from Lecture 3 psfile , pdffile  
Lecture 4, Tuesday, October 8, 2013 Topological classification of compact Riemann surfaces, holomorphic maps between compact Riemann surfaces. Degree of a holomorphic map between compact Riemann surfaces. 
Exercises from Lecture 4 psfile , pdffile  
Lecture 5, Tuesday, October 15, 2013 Degree of a holomorphic map between compact Riemann surfaces. Divisors. 
Exercises from Lecture 5 psfile , pdffile  
Lecture 6, Tuesday, October 22, 2013 Sheaves of modules associated to divisors, RiemannRoch space and its finite dimensionality. 
Exercises from Lecture 6 psfile , pdffile  
Lecture 7, Tuesday, October 29, 2013 Stalks of the structure sheaf, cotangent space, differentials. 
Exercises from Lecture 7 psfile , pdffile  
Lecture 8, Tuesday, November 5, 2013 Holomorphic and meromorphic differential forms. 
Exercises from Lecture 8 psfile , pdffile  
Lecture 9, Tuesday, November 12, 2013 Genus of a compact Riemann surface. The RiemannRoch formula. The RiemannHurwitz fomula. Coverings and universal coverings. Holomorphic maps of complex tori. 
Exercises from Lecture 9 psfile , pdffile  
Lecture 10, Tuesday, November 19, 2013 Holomorphic maps of complex tori. Isomorphism classes of complex tori. 
Exercises from Lecture 10 psfile , pdffile  
Lecture 11, Tuesday, November 26, 2013 Meromorphic functions on complex tori. 
Exercises from Lecture 11 psfile , pdffile  
Lecture 12, Tuesday, December 3, 2013 Complex tori as algebraic curves. jinvariant. 
Exercises from Lecture 12 psfile , pdffile  
Lecture 13, Tuesday, December 10, 2013 Integration of differential forms along curves, residue theorem and its inverse. 
Exercises from Lecture 13 psfile , pdffile  
Lecture 14, Tuesday, December 17, 2013 Jacobian of a compact Riemann surface of positive genus. AbelJacobi theorem and its first corollaries. Compact Riemann surfaces as projective algebraic varieties. 
Exercises from Lecture 14 psfile , pdffile 
Fundamental group. A chapter of the Algebraic topology book by Allen Hatcher.  
Topological classification of surfaces by Richard Koch. 

A note on summability (in German) by Günther Trautmann. 
Forster, Otto.  Lectures on Riemann surfaces; transl. by Bruce Gilligan, New York: SpringerVerlag, 1999.  
Schlichenmaier, Martin.  An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces, Berlin: Springer, 2007.  
Freitag, Eberhard; Busam, Rolf.  Complex analysis. Transl. from the German by Dan Fulea, Berlin: Springer, 2009.  
Freitag, Eberhard.  Complex analysis 2. Riemann surfaces, several complex variables, Abelian functions, higher modular functions, Berlin: Springer, 2011.  
Miranda, Rick.  Algebraic curves and Riemann surfaces, Providence RI: American Mathematical Society, 1995.  
Farkas, Hershel M.; Kra, Irwin.  Riemann surfaces, Springer, 1992.  
Griffiths, Philip; Harris, Joseph.  Principles of algebraic geometry, New York : J. Wiley, 1994. 