Explore the fundamental concepts of Fourier Transforms in this comprehensive lecture delivered by Rajaram Nityananda as part of the Summer School for Women in Physics 2024. Delve into the mathematical techniques and applications of Fourier analysis, gaining insights into its importance in various fields of physics. Learn how these transforms enable the decomposition of complex signals into simpler components, facilitating the study of wave phenomena, signal processing, and data analysis. Engage with practical examples and problem-solving approaches that demonstrate the power and versatility of Fourier Transforms in scientific research and engineering applications.