DOCUMENTA MATHEMATICA, Extra Volume ICM II (1998), 433-442 W. G. Dwyer Title: Lie Groups and p-Compact Groups A $p$-compact group is the homotopical ghost of a compact Lie group; it is the residue that remains after the geometry and algebra have been stripped away. This paper sketches the theory of $p$-compact groups, with the intention of illustrating the fact that many classical structural properties of compact Lie groups depend only on