For clarity's sake, I'm providing this map of the Stalingrad area and the initial Axis and Soviet positions. http://www.emersonkent.com/map_archive/wwii_advance_stalingrad_1942.htm

The tactical objective of Case Blau, the larger operation of which Stalingrad was a part, was not to "push threw to the Urals," but to seize the Caucasus, the area north of Turkey but south of the Don River. For this operation, the German Army Group South had been split into two pieces, Army Group A and Army Group B. Army Group A was to advance into the Caucasus and capture Soviet oil facilities. Army Group B, meanwhile, was tasked with protecting Army Group A's flank against the Soviet forces east of the Don and Volga Rivers. As part of this operation, the German 6th Army and 4th Panzer Army were ordered to seize the city of Stalingrad, a major crossing on the Volga River and a Soviet manufacturing and logistics hub. The idea was not to go across the Volga at all, but to seize the city and, along with the German 2nd Army, the Romanian 3rd and 4th Armies, the Italian 8th Army, and the Hungarian 2nd Army, hold the Soviets at the line of the Don-Volga.