In mathematics, Weyl's theorem or Weyl's lemma might refer to one of a number of results of Hermann Weyl. These include

• the Peter–Weyl theorem
• Weyl's theorem on complete reducibility, results originally derived from the unitarian trick on representation theory of semisimple groups and semisimple Lie algebras
• Weyl's theorem on eigenvalues
• Weyl's criterion for equidistribution (Weyl's criterion)
• Weyl's lemma on the hypoellipticity of the Laplace equation
• results estimating Weyl sums in the theory of exponential sums
• Weyl's inequality
• Weyl's criterion for a number to be in the essential spectrum of an operator