1.The Complex number system 2. Metric spaces and topology of C 3. Elementary properties and examples of analytic functions 4. Complex integration 5. Singularities 6. The maximum modulus theorem 7. Compactness and convergence in the space of analytic functions 8. Range´s theorem 9. Analytic continuation and Riemann surfaces 10. Harmonic functions 11. Entire functions 12. The range of an analytic funtion