A Concise Course in Galois Theory

Born from years of teaching undergraduate and graduate algebra courses at Chongqing University, this text is designed to introduce Galois theory while minimizing prerequisites. It seeks to reconnect the abstract machinery of modern algeba: groups, rings, and fields with the historical problem that inspired its creation: determining when a polynomial can be solved by radicals. By anchoring abstract concepts in concrete motivation, we hope to illuminate both the ``how" and the ``why" of algebraic structures.