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Designed as a textbook which is important for undergraduate and postgraduate students. This textbook consists three chapters, the first chapter discusses series representation of analytic functions, the second chapter discusses calculus of residues and the third chapter discusess mobius transform of complex function. Each chapter is prepared with simple language to readers for easy understanding. In this textbook the readers can obtain further information about series representation of analytic functions, calculus of residues of complex function, mobius transform of complex function and its real application.