The partition function of 2d string theory

We derive a compact and explicit expression for the generating functional of all correlation functions of tachyon operators in 2D string theory. This expression makes manifest relations of the $c=1$ system to KP flow and $W_{1+\infty}$ constraints. Moreover we derive a Kontsevich-Penner integral representation of this generating functional.Comment: 28 pages, 3 figures not included, harvmac. Preprint IASSNS-HEP-92/48, YCTP-P22-9