For at least 200 years, since the time of Malthus, population growth has been recognized as providing a critical link between the performance of individual organisms and the ecology and evolution of species. We present a theory that shows how the intrinsic rate of exponential population growth, rmax, and the carrying capacity, K, depend on individual metabolic rate and resource supply rate. To do this, we construct equations for the metabolic rates of entire populations by summing over individuals, and then we combine these population-level equations with Malthusian growth. Thus, the theory makes explicit the relationship between rates of resource supply in the environment and rates of production of new biomass and individuals. These individual-level and population-level processes are inextricably linked because metabolism sets both the demand for environmental resources and the resource allocation to survival, growth, and reproduction. We use the theory to make explicit how and why rmax exhibits its characteristic dependence on body size and temperature. Data for aerobic eukaryotes, including algae, protists, insects, zooplankton, fishes, and mammals, support these predicted scalings for rmax. The metabolic flux of energy and materials also dictates that the carrying capacity or equilibrium density of populations should decrease with increasing body size and increasing temperature. Finally, we argue that body mass and body temperature, through their effects on metabolic rate, can explain most of the variation in fecundity and mortality rates. Data for marine fishes in the field support these predictions for instantaneous rates of mortality. This theory links the rates of metabolism and resource use of individuals to life-history attributes and population dynamics for a broad assortment of organisms, from unicellular organisms to mammals.