This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year's course, and the choice of material treated is reasonably standard and should be satisfactory for most first courses in complex analysis. The approach to each topic appears to be carefully thought out both as to mathematical treatment and pedagogical presentation, and the end result is a very satisfactory book for classroom use or self-study

1.the complex number system 2.metric spaces and the 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.runge's therem 9.analytic continuation and riemann surfaces 10.harmonuc functions 11.entire functions 12.the range of an analytic function TABLE OF CONTENTS,VOLUME II 13.return to basics 14.conformal equivalence for simply connected regions 15.conformal equivalence for finitely connected regions 16.analytic covering maps 17.de branges's proof of the bieberbach conjecture 18.some fundamental conceps from analysis 19.harmonic functions redux 20.hardy spaces on the disk 21.potential theory in the plane

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