What was the famous battle in October of 1942 in Egypt? Who won and why?
The Battle of El Alamein between Axis and British forces.
The battle of El Alamein was the high tide point of the expansion of the Axis forces (Germany and Italy) in North Africa and resulted in their defeat.
The British forces led by General B. L Montgomery after containing the attack from the Axis forces smashed into the lines of the Afrika Korps and Italian Army causing a general retreat and the capture of huge numbers of prisoners and hardware.
The reasons for this victory are various:
the Afrika Korps and Italian Army were far from their bases making their supply line too long in a desert that was not easy to cross and prone to disruption by, for example, enemy air attacks; on top of this the intense submarine/naval/air warfare in the Mediterranean from the British assured that very few cargoes and supplies could reach the troops fighting in North Africa (the British were able to "read" the secret messages of the German Army that erroneously attributed the leaking of information to treacherous activities of the Italians!);
the British were placed very near their bases and supply points (in Egypt) and could summon more tanks (Sherman and Grant from the USA), ammunitions, airplanes and food/water;
the British had a new commander, General Montgomery, that was particularly suited for this kind of battle being a very methodical and very careful organizer in dealing with the training and logistic. Montgomery didn`t leave nothing to improvisation and made sure to have an overwhelming superiority before attacking. On top of it, to deplete the Axis attack, he placed a "sea" of mines in front of the British positions where the German tanks were decimated and immobilized cutting the momentum of the Afrika Korps.
In the battles of North Africa the key feature was mobility. The German commander, E. Rommel, considered the desert as a sea where “fleets” of armored troops (tanks/armored troop carriers and lorries) moved as ships engaging in a kind of naval battles; but, to be able to do that you needed fuel and mobility; once the Germans were denied both in front of El Alamein. The terrain was against the mobility preferred by Rommel. The Qattara Depression blocked movement to the south, rugged mountains the Alam Halfa divided the land between the impassible depression and the ocean in half. (not enough fuel, mines that made movement of tanks impossible, almost immobile Italian Army with to transportation and few obsolete tanks) the Axis attack crumbled and the following British counter attack completely demolished the Axis front and armies.
[ Field Marshal Bernard Montgomery.]