Textbook in PDF format This volume provides a rigorous and accessible introduction to the foundations of complex analysis for undergraduate mathematics students. Designed for university courses, self-study, and professional reference, it balances mathematical precision with pedagogical clarity. What You Will Learn Complex numbers: definitions, algebraic and geometric properties. Polar form, argument, powers and roots (De Moivre's Theorem). Sets of points in the complex plane. Complex functions: mappings, continuity, holomorphic functions. Conformal mappings and Laurent series. Applications in physics and engineering. Key Features 512 pages of structured academic content. 308 fully solved problems with step-by-step proofs. Real-world applications: electrical circuits, wave propagation, fluid dynamics, and fractals. Exercises ranging from foundational to research-level difficulty. Part of the Mathematics Undergraduate Series — Bachelor's Degree in Mathematics. Who Is This Book For ? Undergraduate and graduate students of mathematics, physics, and engineering seeking a complete and rigorous treatment of complex variable functions. Also suitable as a reference for professors and researchers