In mathematics, and particularly singularity theory, the Milnor number, named after John Milnor, is an invariant of a function germ.
If f is a complex-valued holomorphic function germ then the Milnor number of f, denoted μ(f), is either a nonnegative integer, or is infinite. It can be considered both a geometric invariant and an algebraic invariant. This is why it plays an important role in algebraic geometry and singularity theory.