Needham T. Visual Complex Analysis

Clarendon Press, Oxford, 1997. - 592 p.This radical first course on complex analysis brings a beautiful and powerful
subject to life by consistently using geometry (not calculation) as the means of explanation.
Although aimed at the complete beginner, professional mathematicians and physicists
may also enjoy the fresh insights afforded by this unusual approach. The book contains: new geometric arguments that yield a more intuitive and elementary approach than the conventional,
over 500 diagrams to illuminate the geometric reasoning, no advanced prerequisites, unusually wide-ranging exercises that investigate important and interesting facts, penetrating (yet elementary) treatments of such important topics as Mobius transformations, non-Euclidean geometry, the vector-field interpretation of complex integration, ways to harness the power of the modern PC, both to witness general theorems in action, and to gain further theoretical insights.