Abstract Algebra - From Group Theory to Galois Theory

A structural approach to abstract algebra, providing a transparent and mathematically sound introduction to groups, rings, and fields. The text is built on the philosophy that abstraction should never be divorced from algorithmic computation; every abstract definition is paired with a computational constraint or a highly verifiable example to ensure deep intuition. The first semester focuses on Group Theory, culminating in the Isomorphism Theorems, while the second semester develops the factorization properties of integral domains and Field Theory. The text concludes with a comprehensive treatment of Galois Theory, where students experience the climax of the undergraduate sequence, observing the synthesis of group and field theory as subgroups perfectly mirror intermediate extensions.