This book is compiled as one of the reading resource books on courses in Complex Variable Functions and Variable Functions Advanced Complex, so it can help students majoring in Mathematics, Mathematics, and Engineering Education in understanding and developing existing concepts in those courses. The material in the book is presented as simple as possible, but in the discussion still emphasis on conceptual skills. In addition, the author also remains to include some examples as well as exercises that is testing the skills of calculation and application This book consists of 8 Chapters containing numbers complexes, complex functions, elementary transformations, functions analytics, complex integralization, complex series, residue theory, and residual application. This book has the advantage of being able to improves a deeper understanding of concepts because In its discussion, several theorems are supplemented by simple evidence and examples.