In abstract algebra, a **magma** is a particularly simple kind of algebraic structure.

Specifically, a magma consists of a set with a single binary operation on it, which is usually (but not always) interpreted as a kind of multiplication. No axioms are required of the operation for it to define a magma. Magmas are not often studied as such; instead there are several different kinds of magmas, depending on what axioms one might require of the operation. Commonly studied types of magmas include:

- quasigroups -- nonempty magmas where division is always possible;
- loopss -- quasigroups with identity elements;
- semigroups -- magmas where the operation is associative;
- monoids -- semigroups with identity elements;
- groupss -- monoids with inverse elements, or equivalently, associative quasigroups (which are always loops);
- abelian groups -- groups where the operation is commutative.

There is such a thing as a **free magma** on any set *X*. It can be described, in terms familiar in computer science, as the magma of binary trees with leaves labelled by elements of *X*, with operation the joining of trees at the root. It therefore has a foundational role in syntax.