This is a concise textbook of complex analysis for undergraduate and graduate students. It has been written from the viewpoint of modern mathematics - the conjugate delta-equation, differential geometry, Lie groups, etc. It contains all the traditional material on complex analysis, but many statements and proofs of classical theorems in complex analysis have been made simpler, shorter and more elegant due to modern mathematical ideas and methods. For example, the Mittag-Leffler theorem is proved by the conjugate delta-equation, the Picard theorem is proved using the methods of differential geometry, and so on.

Calculus; Cauchy Integral Theorem and Cauchy Integral Formula; Theory of Series of Weierstrass; Riemann Mapping Theorem; Differential Geometry and Picard Theorem; Elementary Facts on Several Complex Variables.

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