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A binary [[Algebraic operation|algebraic operation]]. 

The composition (or superposition) of two functions $f:Y \rightarrow X$ and $g:Z \rightarrow Y$ is the function $h=f\circ g : Z \rightarrow X$, $h(z)=f(g(z))$. 

The composition of two [[binary relation]]s $R$, $S$ on set $A \times B$ and $B \times C$ is the relation $T = R \circ S$ on $A \times C$ defined by $a T c \Leftrightarrow \exists b \in B \,:\, a R b, b S c$.

See [[Convolution of functions]] concerning composition in probability theory.

See [[Automata, composition of]] concerning composition of automata.

See also: [[Composition (combinatorics)]], an expression of a natural numbers as an ordered sum of positive integers; [[Composition series]], a maximal linearly ordered subset of a partially ordered set.