The study of mathematical structure through groups, rings, fields, and their operations.
A group is a set with an associative binary operation, identity element, and inverses
A ring extends groups with a second operation (addition and multiplication)
A field is a ring where every nonzero element has a multiplicative inverse
homomorphisms are structure-preserving maps between algebraic objects
Galois theory connects field extensions to group symmetry, resolving solvability of polynomials
Boolean algebra underpins logic, digital circuits, and set theory
Foundation of cryptography, number theory, linear algebra, and category theory
Related:: geometry, topology, combinatorics, game theory