The aim of the book is to give a smooth analytic continuation from calculus to complex analysis by way of plenty of practical examples and worked-out exercises. The scope ranges from applications in calculus to complex analysis in two different levels.If the reader is in a hurry, he can browse the quickest introduction to complex analysis at the beginning of Chapter 1, which explains the very basics of the theory in an extremely user-friendly way. Those who want to self-study on complex analysis can go through Chapter 1 in which the two main streams of the theory — the power series method due to Weierstrass and the integration method due to Cauchy — are presented in a very concrete way with rich examples. Readers who want to learn more about applied calculus can read Chapter 2, where a lot of practical applications are given. The reader can go through examples and solve the problems following the patterns given in the examples. The book helps the reader to acquire basic skills of complex analysis and its applications. It also gives a smooth introduction to Fourier analysis as well as a quick prelude to thermo- and fluid dynamics, information theory, and control theory.One of the main features of the book is that it presents different approaches to the same topic, helping the reader gain deeper comprehension.