In mathematics, a C₀-semigroup, also known as a strongly continuous one-parameter semigroup, is a generalization of the exponential function. Just as exponential functions provide solutions of scalar linear constant coefficient ordinary differential equations, strongly continuous semigroups provide solutions of linear constant coefficient ordinary differential equations in Banach spaces. Such differential equations in Banach spaces arise from e.g. delay differential equations and partial differential equations.

Formally, a strongly continuous semigroup is a representation of the semigroup (R₊, +) on some Banach space X that is continuous in the strong operator topology. Thus, strictly speaking, a strongly continuous semigroup is not a semigroup, but rather a continuous representation of a very particular semigroup.