First Part. - I The Complex Plane and Elementary Functions. - II Analytic Functions. - III Line Integrals and Harmonic Functions. - IV Complex Integration and Analyticity. - V Power Series. - VI Laurent Series and Isolated Singularities. - VII The Residue Calculus. - Second Part. - VIII The Logarithmic Integral. - IX The Schwarz Lemma and Hyperbolic Geometry. - X Harmonic Functions and the Reflection Principle. - XI Conformal Mapping. - Third Part. - XII Compact Families of Meromorphic Functions. - XIII Approximation Theorems. - XIV Some Special Functions. - XV The Dirichlet Problem. - XVI Riemann Surfaces. - Hints and Solutions for Selected Exercises. - References. - List of Symbols. Language: English