LUCY: A Clifford algebra approach to spinor calculus. LUCY is an algebra package for Maple V release 2/3, which is designed to perform calculations in Clifford bundles of real or complex (simple) Clifford algebras. The authors present the abilities of LUCY giving theory sections followed by specific illustrative examples, which also explain the syntax of the package. LUCY covers e.g. arbitrary user defined bases, multilinearity of the product, spinors and their duals with respect to several involutions, spinor inner products, an easy transition between abstract and matrix algebra and vice versa, spinor connections. The package is thus well suited to explore the Dirac operator on flat and curved manifolds.