Any one of the numerous types of mathematical object studied in algebra and especially in universal algebra;
a mathematical object comprising a carrier set (aka underlying set or domain), an optional scalar set, a set of operations (typically binary operations, but otherwise each of finite arity) and a set of identities (axioms) which the operations must satisfy.
A branch of mathematics dealing with equational classes of algebras, where similar theorems from disparate branches of algebra are unified.
An algebraic structure studied therein.