Polyhedra are geometric representations of linear systems of equations and inequalities. Since polyhedra are used to represent the iteration domains of nested loop programs, procedures for operating on polyhedra can be used for doing loop transformations and other program restructuring transformations which are needed in parallelizing compilers. Thus a need for a library of polyhedral operations has recently been recognized in the parallelizing compiler community. Polyhedra are also used in the definition of domains of variables in systems of affine recurrence equations (SARE). ALPHA is a language which is based on the SARE formalism in which all variables are declared over polyhedral domains consisting of finite unions of polyhedra. This thesis describes a library of polyhedral functions which was developed to support the ALPHA langauge environment, and which is general enough to satisfy the needs of researchers doing parallelizing compilers. This thesis describes the data structures used to represent domains, gives the motivations for the major design decisions that were made in creating the library, and presents the algorithms used for doing polyhedral operations. A new algorithm for recursively generating the face lattice of a polyhedron is also presented. This library has been written and tested, and has be in use since the first quarter of 1993. It is used by research facilities in Europe and Canada which do research in parallelizing compilers and systolic array synthesis. The library is freely distributed by ftp. / Graduation date: 1994