Current attempts to find a unified theory that would reconcile Einstein's
General Relativity and Quantum Mechanics, and explain all known physical
phenomena, invoke the Kaluza-Klein idea of extra spacetime dimensions. The best
candidate is M-theory, which lives in eleven dimensions, the maximum allowed by
supersymmetry of the elementary particles. We give a non-technical account.
An Appendix provides an updated version of Edwin A. Abbott's 1884 satire {\it
Flatland: A Romance of Many Dimensions}. Entitled {\it Flatland, Modulo 8}, it
describes the adventures of a superstring theorist, A. Square, who inhabits a
ten-dimensional world and is initially reluctant to accept the existence of an
eleventh dimension.Comment: Oskar Klein Professorship Inaugural Lecture, University of Michigan,
16 March 2001. 38 pages, Latex, 15 color figure
