As early as December 18, 1940, Hitler's Directive Number 21 called for the German Army "to erect a barrier against Asiatic Russia on the general line Volga-Archangel."
The actual attack--code named Barbarossa--didn't begin until June 22, 1941. The aim was to destroy the Red Army completely, and penetrate far enough into Soviet territory to prevent Soviet air reprisals against Germany. Intending to take only six months, the battles--stretched out along an 1800 mile front, from the Arctic Ocean to the Caucasus--lasted until Germany's ultimate defeat in 1945.
Source: The Simon and Schuster Encyclopedia of World War II, Edited by Thomas Parrish, Brig. Gen. S.L.A. Marshall, chief Consultant Editor, Simon and Schuster, New York: 1978