Short answers, pulled from the story.
The Battle of Gazala was fought from the 26th of May to the 21st of June 1942, during the Western Desert Campaign of the Second World War. It took place near the village of Gazala, west of the port of Tobruk in Libya.
Panzerarmee Afrika was commanded by Generaloberst Erwin Rommel, with the Deutsches Afrika Korps under Generalleutnant Walter Nehring. The British Eighth Army was commanded by General Neil Ritchie, under the overall authority of General Sir Claude Auchinleck as Commander-in-Chief Middle East.
The Gazala Line was a series of brigade-sized defensive boxes stretching from the coast at Gazala, 48 km west of Tobruk, to the old Ottoman fortress at Bir Hakeim 80 km inland to the south. The boxes were separated by minefields and wire and connected by patrols. The Allies had 110,000 men, 843 tanks, and 604 aircraft along the line and in reserve.
The 1st Free French Brigade under Brigadier Marie-Pierre Koenig defended Bir Hakeim for roughly ten days after the Axis flanking move began, repelling multiple attacks using 75 mm guns and extensive minefields. Rommel's own account acknowledged that Axis attacks repeatedly bogged down in the French fortifications. The position was not overrun until the 10th of June 1942.
Panzerarmee Afrika penetrated a weak spot on the eastern defensive perimeter of Tobruk and took the port within twenty-four hours. The garrison of 33,000 men was captured along with over 1,000 vehicles in working order, 5,000 long tons of food, and 1,400 long tons of petrol. It was the largest capitulation of British Empire forces since the fall of Singapore in February 1942.
The Eighth Army suffered around 50,000 casualties, including approximately 35,000 prisoners taken at Tobruk. German losses were roughly 3,360 men, about 15 percent of their force. Italian casualties included 3,000 men and 125 tanks. It was estimated that there were 1,188 tank casualties on the Allied side across 17 days of fighting.
Hitler promoted Rommel to the rank of field marshal following the capture of Tobruk, making him the youngest German officer ever to achieve that rank. Rommel reportedly remarked that he would have preferred another panzer division. The Battle of Gazala is considered the greatest victory of his career.