Final answer:
The major battles during Hitler's invasion of the Soviet Union were the Siege of Leningrad, the Battle for Moscow, and especially the pivotal Battle of Stalingrad, followed by the large tank engagement at the Battle of Kursk, which marked the turning point on the Eastern Front.
Step-by-step explanation:
When Hitler invaded the Soviet Union, the major battles and sieges included the catastrophic Siege of Leningrad, the Battle for Moscow, and most famously, the Battle of Stalingrad.
Operation Barbarossa, the code name for the invasion, resulted in a series of initial successes for the Wehrmacht but eventually turned disastrous as the German forces were unprepared for the harsh Russian winter and vast distances involved.
The Battle of Stalingrad became the pivotal turning point, where the Soviet Red Army, under the command of General Georgy Zhukov, conducted a brilliant counter-encirclement, trapping the German 6th Army. A combination of tenacious defense by the Soviets and the harsh winter led to a catastrophic German defeat.
Another significant engagement was the Battle of Kursk, the largest tank battle in history which took place in the summer of 1943. Following the Soviet victory at Stalingrad, this battle marked a critical point in which the German forces were forced onto the defensive, leading to a steady Soviet push westwards.
This battle, along with others on the Eastern Front, contributed significantly to the weakening of Germany's military capabilities and the eventual turning of the tide in World War II.