Wiktionary
n. (context mathematics English) The branch of mathematics concerned with algebraic structures, such as groups, rings, and fields.
Wikipedia
Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory is a powerful formalism for analyzing and comparing different algebraic structures.
Universal algebra is a related subject that studies the nature and theories of various types of algebraic structures as a whole. For example, universal algebra studies the overall theory of groups, as distinguished from studying particular groups.
Usage examples of "abstract algebra".
If cryptography is a form of abstract algebra, then inventing a new cipher system is nothing more than building abstract castles in the air with material and design of one's own choosing.