We will use the book "Complex Analysis" by Theodore W. Gamelin, Springer Verlag.
The syllabus is:
Chapter 1: The complex plane and elementary functions
Chapter 2: Analytic functions.
Chapter 3: Line integrals and harmonic functions - Sections 1, 2, 3, 4, 5, 6.
Chapter 4: Complex integration and analyticity - Sections 1, 2, 3, 4, 5.
Chapter 5: Power series - Sections 1, 2, 3, 4, 5, 6, 7.
Chapter 6: Laurent series and isolated singularities - Sections 1, 2, 3, 4.
Chapter 7: The residue claculus - Sections 1, 2, 3, 4.
Chapter 8: The logarithmic integral - Sections 1, 2, 5, 8.
Chapter 9: The Schwarz lemma - Sections 1, 2.
Chapter10: Harmonic functions - Sections 1, 2.
Chapter 2: Analytic functions.
Chapter 3: Line integrals and harmonic functions - Sections 1, 2, 3, 4, 5, 6.
Chapter 4: Complex integration and analyticity - Sections 1, 2, 3, 4, 5.
Chapter 5: Power series - Sections 1, 2, 3, 4, 5, 6, 7.
Chapter 6: Laurent series and isolated singularities - Sections 1, 2, 3, 4.
Chapter 7: The residue claculus - Sections 1, 2, 3, 4.
Chapter 8: The logarithmic integral - Sections 1, 2, 5, 8.
Chapter 9: The Schwarz lemma - Sections 1, 2.
Chapter10: Harmonic functions - Sections 1, 2.