Weyl is an extensible algebraic manipulation substrate that has been designed to represent all types of algebraic objects. It deals not only with the basic symbolic objects like polynomials, algebraic functions and differential forms, but can also deal with higher level objects like groups, rings, ideals and vector spaces. Furthermore, to encourage the use of symbolic techniques within other applications, Weyl is implemented as an extension of Common Lisp using the Common Lisp Object Standard so that all of Common Lisp’s facilities and development tools can be used in concert with Weyl’s symbolic tools.