Author: Dr. Sourayan Banerjee (IIT Kharagpur), Aritra Dey (TIFR Mumbai). Edited by Shilpa Bera.

Most math textbooks present theorems as finished monuments, hiding the messy scaffolding and false starts that drove their creators. This book takes the opposite approach. Designed for undergraduate students, it is an active invitation to logical discovery. Group theory did not begin with abstract definitions; it grew from concrete, frustrating puzzles about polynomial roots, geometric symmetries, and number patterns. The abstraction was the destination, not the starting point. This short guide is built entirely around that problem-driven journey. Each chapter begins with a motivating puzzle rather than a dry definition. We only formalise a tool—like a subgroup, coset, or isomorphism—when the problem demands it. To bridge the gap between intuition and exam performance, we integrate solved problems drawn directly from premier Indian M.Sc. and Ph.D. entrance tests, including IIT JAM, NBHM, and TIFR. By tackling these elite questions within a conceptual framework, you will build both deep mathematical intuition and the problem-solving speed needed to clear these exams.

Every student of mathematics knows the feeling. You are working through a difficult problem set, or studying for a major exam like TIFR or NBHM, and you suddenly need to verify a quick structural property. At that exact moment, opening a massive, thousand-page abstract algebra encyclopedia can feel overwhelming. You do not need to relearn the entire history of the subject; you just need a reliable, quick reference to spark your memory. That is why we wrote this book. As authors, our vision was to create a companion for students—a book you can readily refer to for revising what you have already learned in your respective classes, colleges, or separate courses. The mathematical world is already blessed with truly legendary, comprehensive textbooks on abstract algebra. This book is not meant to compete with them, nor is it meant to teach you group theory from scratch. Instead, its sole purpose is to be that trusted ``pocket edition" that you can carry with you everywhere. Whether you are riding the train, sitting in a cafe between lectures, or doing a final review the night before a competitive test, we hope this little book serves as the perfect bridge between what you were taught and what you need to remember. In a world where you can instantly look up any theorem on the internet, there is still something unmatched about flipping open a physical page. The internet gives you thousands of scattered search results, but this book gives you the exact, trusted mathematical insight you need without the digital noise or distraction. Keep it in your bag, use it often, and may it make your mathematical journey just a little bit smoother.