This book is your gateway to understanding Fourier integrals, Fourier transforms & complex analysis the core tools behind modern engineering systems. With plenty of worked out examples, practice exercises and a model question paper, its designed to help you learn by doing. Inside you'll journey through Fourier integrals, Fourier transforms, and the rich world of complex analysis. From mastering complex integration techniques to exploring the elegance of contour integrals and residue calculus, each concept is broken down ans brought to life through clear explanation and practical insights. This book is designed to serve as a comprehensive guide for students ans educators seeking to deepen their understanding of the subject. Special attention has given to the third semester B.Tech degree syllabus (2024 Scheme) of the APJ Abdul Kalam Technological University.