A statistical mechanical theory of collective dynamic barriers, slow segmental relaxation, and the glass transition of polymer melts is developed by combining, and in some aspects extending, methods of mode coupling, density functional, and activated hopping transport theories. A coarse-grained description of polymer chains is adopted and the melt is treated as a liquid of segments. The theory is built on the idea that collective density fluctuations on length scales considerably longer than the local cage scale are of primary importance in the deeply supercooled regime. The barrier hopping or segmental relaxation time is predicted to be a function primarily of a single parameter that is chemical structure, temperature, and pressure dependent. This parameter depends on the material-specific dimensionless amplitude of thermal density fluctuations (compressibility) and a reduced segmental density determined by the packing length and backbone characteristic ratio. Analytic results are derived for a crossover temperature T-c, collective barrier, and glass transition temperature T-g. The relation of these quantities to structural and thermodynamic properties of the polymer melt is established. A universal power-law scaling behavior of the relaxation time below T-c, is predicted based on identification of a reduced temperature variable that quantifies the breadth of the supercooled regime. Connections between the ratio T-c/T-g, two measures of dynamic fragility, and the magnitude of the local relaxation time at T-g logically follow. Excellent agreement with experiment is found for these generic aspects, and the crucial importance of the experimentally observed near universality of the dynamic crossover time is established. Extensions of the theory to treat the full chain dynamics, heterogeneity, barrier fluctuations, and nonpolymeric thermal glass forming liquids are briefly discussed. (C) 2004 American Institute of Physics.