We discuss the Mott-Hubbard transition in light of the Hubbard model i
n infinite dimensions with special emphasis on the finite-temperature
aspects of the problem. We demonstrate that the Mott transition at fin
ite temperatures has a first-order character. We determine the region
where metallic and insulating solutions coexist using second-order per
turbation theory and we draw the phase diagram of the Hubbard model at
half filling with a semicircular density of states. We discuss the le
ssons learned from the present treatment of the Hubbard model and the
connection to other approximation schemes and to experiments on transi
tion-metal oxides.