This book, An Introduction to Fourier Series: Theory and Examples, is designed to provide a clear and systematic introduction to the theory of Fourier series for undergraduate students of mathematics, engineering, and related disciplines. The primary objective of the book is to develop a strong conceptual foundation while simultaneously strengthening problem-solving skills through a large number of worked examples. The text begins with preliminary concepts and gradually introduces the fundamental ideas of Fourier series, Euler’s formulae, and the determination of Fourier coefficients. Special attention is given to important topics such as functions with points of discontinuity, change of interval, even and odd functions, and half-range expansions. These topics are explained in a logical and student-friendly manner to ensure ease of understanding. Further chapters deal with the complex form of Fourier series, Parseval’s identity, and practical harmonic analysis, highlighting their mathematical significance and practical relevance. Each chapter is supported by illustrative examples and exercises, which help readers to understand the application of theoretical concepts and to prepare effectively for university examinations. The presentation throughout the book emphasizes clarity, simplicity, and consistency. Mathematical derivations are explained step by step, and standard notation is used to maintain compatibility with commonly prescribed syllabi. This book is intended to serve as a reliable introductory text as well as a useful reference for students seeking a thorough understanding of Fourier series through theory and examples. --- Step 3 --