Frank H. Stillinger AT&T Bell Laboratories, Murray Hill, New Jersey 07974 Science; Mar 31, 1995; 267, 5206; pg. 1935 Abstract Various static and dynamic phenomena displayed by glass-forming liquids, particularly those near the so-called "fragile" limit, emerge as manifestations of the multidimensional complex topography of the collective potential energy function. These include nonArrhenius viscosity and relaxation times, bifurcation between the a- and b-relaxation processes, and a breakdown of the Stokes-Einstein relation for self-diffusion. This multidimensional viewpoint also produces an extension of the venerable Undemann melting criterion and provides a critical evaluation of the popular "ideal glass state" concept.