Dealing with complex numbers and functions of a complex variable, which hold a decisive place in the historical development of mathematics and are widely used in many applied fields primarily engineering this book approaches the subject in an order aligned with its historical evolution, presenting an accessible coverage with simple explanations and numerous examples rather than relying on advanced mathematical formalism. The solved problems included after each topic significantly contribute to reinforcing the reader's understanding. In particular, the residue theorem, which is of critical importance in engineering applications, is comprehensively covered in the book; furthermore, the final chapter details the fundamentals of singular integral equations through detailed examples within the framework of advanced applications of complex variable functions. Prepared by leveraging the word-derivation and phonetic advantages of the Turkish language, this work appeals to mathematics and engineering readers at both the undergraduate and graduate levels.