The attached paper is a description of the LISP system starting with the machine-independent system of recursive functions of symbolic expressions. This seems to be a better point of view for looking at the system than the original programming approach. After revision, the paper will be submitted for publication in a logic or computing journal. This memorandum contains only the machine independent parts of the system. The representation of S-expressions in the computer and the system for representing S-functions by computer subroutines will be added.