This edition presents the theory of functions of a complex variable with clear aims: to introduce beginning students to both the geometric and analytic viewpoints. It blends Riemann’s geometric approach with Weierstrassian rigor, showing how each method contributes to understanding complex functions.

Topics move from the basics of complex numbers and their geometric representation to single-valued analytic functions, the exponential and trigonometric functions, and the ideas behind conformal representations. The text also surveys the RIEMANN surface, the notion of analytic continuation, and related theorems that structure the subject.

Foundations: complex numbers, geometry, and basic representations
Analytic theory: regular functions, derivatives, and integrals
Special functions: exponential, sine, cosine, and their identities
Conformal mappings and geometric transformations
Introductory concepts of the RIEMANN surface and analytic continuation

Ideal for readers beginning a study of complex analysis or seeking a solid, practical overview of the subject.

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