Lectures:  Exercises:  
Lecture 1, Tuesday, September 20, 2011 Definition of Riemann surfaces, first examples and properties. 
Exercises from Lecture 1 psfile , pdffile  
Lecture 2, Tuesday, September 27, 2011 Meromorphic functions, elementary properties of holomorphic maps. 
Exercises from Lecture 2 psfile , pdffile  
Lecture 3, Tuesday, October 4, 2011 Homotopy of curves, fundamental group, coverings, holomorphic maps of Riemann surfaces as ramified coverings. 
Exercises from Lecture 3 psfile , pdffile  
Lecture 4, Tuesday, October 11, 2011 Universal coverings, deck transformations, divisors. 
Exercises from Lecture 4 psfile , pdffile  
Lecture 5, Tuesday, October 18, 2011 Sheaves of modules associated to divisors, RiemannRoch space and its finite dimensionality. 
Exercises from Lecture 5 psfile , pdffile  
Lecture 6, Tuesday, October 25, 2011 Holomorpic and meromorphic differential forms. 
Exercises from Lecture 6 psfile , pdffile  
Lecture 7, Tuesday, November 8, 2011 The theorem of RiemannRoch, first corollaries, meromorphic functions on complex tori. 
Exercises from Lecture 7 psfile , pdffile  
Lecture 8, Tuesday, November 15, 2011 Field of meromorphic functions on complex tori, complex tori as plane projective curves. Correction: description of even elliptic functions with the poles on the lattice: psfile , pdffile. 
Exercises from Lecture 8 psfile , pdffile  
Lecture 9, Tuesday, November 22, 2011 Integration of differential forms along curves, residue theorem. Correction: mistake in the definition of integral: psfile , pdffile. 
Exercises from Lecture 9 psfile , pdffile  
Lecture 10, Tuesday, November 29, 2011 Corollaries of the residue theorem. Proof of the RiemannRoch theorem: preparatory work. 
Exercises from Lecture 10 psfile , pdffile  
Lecture 11, Tuesday, December 6, 2011 Topological classification of compact Riemann surfacess, periods, proof of the RiemannRoch theorem, Jacobian of a compact Riemann surface. 
Exercises from Lecture 11 psfile , pdffile  
Lecture 12, Tuesday, December 13, 2011 Abel's theorem and its first corollaries, Jacobi's theorem, remarks on the classification of compact Riemann surfaces of genus 1, divisors and invertible sheaves. 
Exercises from Lecture 12 psfile , pdffile 
Please let me know about misprints and/or mistakes found in the exercises and the lectures.
Some relevant links:
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. 