Functional calculi A functional calculus is a construction which associates with an operator or a family of operators a homomorphism from a function space into a subspace of continuous linear operators i.e. a method for defining functions of an operator . Perhaps the most familiar example is based on the spectral theorem for bounded self adjoint operators on a complex Hilbert space. This book contains an exposition of several such functional calculi. In particular there is an exposition based on the spectral theorem for bounded self adjoint operators an extension to the case of several commuting self adjoint operators and an extension to normal operators. The Riesz operational calculus based on the Cauchy integral theorem from complex analysis is also described. Finally an exposition of a functional calculus due to H. Weyl is given