I've looked around and I just can't find it (most of the sites I found are too busy giving tongue baths to Eisenhower). I read somewhere that a big strategy was to go after Rommel's fuel and smash it, preventing him from keeping his tanks on the field, but what happened in Africa? For some reason, the textbooks never seem to mention what they actually DID in the various theaters...
Before the Germans entered the African front, the Italians were getting destroyed. The British under Archibald wavell had repulsed the Initial Italian offensive launched by the Italian commander Grazini. The British nearly drove the Italians out of Libya completely. That is when Rommel came to North Africa by way of tripoli ( the main axis supply base in North Africa). The British also had much of their men redeployed to Greece. The British dug in expecting the Italians and Germans to do the same. However, Rommel attacked unexpectedly and this started the whole back and forth struggle that wouldn't end until 1943.
Until Rommel arrived ad counterattack the British and Italian strategy was basically the same. Send the main force along the coast while armoured and motorized units flanked through the dessert. However, under Montgomery the strategy changed to where the British would build up men and supplies and force a decisive battle that they could win. The 2nd battle of El Alamein was an example of this.
Sources:
The Second World War by John Keegan (I really recommend this if you want more of a battle focuses outlook on the war)
Hey, I wish I haf the time to write a response on the other fronts (and I might be able to later) but in the mean time, I hope this answer I did previously about East Africa specifically will be of interest to you!
Italy managed to occupy Ethiopia pretty quickly in the Second Italo-Abyssinian War in 1935-1936, and Selassie was forced to flee his country on May 2nd, 1936. This was actually a major reason Italy left the League of Nations, since he made his way to Geneva (with the help of the UK) and was allowed to speak to the body, which really angered Italy.
With Italy's entry into World War II in mid-1940, she hoped to expand this territory, briefly capturing British Somaliland and threatening the Sudan. Early hopes for their invasion through the western desert were that Italian forces could sweep through Egypt and link up with their East African forces. Obviously, this failed though, and the East African Forces were essentially on their own. The British regrouped, and with the help of commonwealth and colonial forces, as well as Ethiopian forces, they counterattacked in early 1941. The Italians were pretty overwhelmed, and the Allies swept into Ethiopia. By May 5th, coincidentally exactly five years after the Italians captured it, Hallie Selassie was able to return into Addis Ababa, the capital. Major combat did continue though, and it wasn't until late November that the last major Italian force in East Africa surrendered, following defeat at Gondar.
Following the general surrender, there was still a low level insurgency/guerilla war being fought in the region by small units of Italians who had chosen to continue to fight, mostly fascist Blackshirts who were the most committed to the Italian cause. This mostly came to an end by late-1943 though with Italy's capitulation.
An interesting sidenote, but the British weren't particularly inclined in restoring the full sovereignty of Ethiopia, and only really agreed to the Anglo-Ethiopian Agreement with some prodding from the USA.
Sources: The Italian Invasion of Abyssinia
And some date checking on Wikipedia.
The purpose of the African campaign was to keep control of the Mediterranean Sea and area in North Africa to be used for a southern European attack. Regarding strategy there really is none as they were battling of a 50 mine wide tract of desert. On the 8th of April 1942 Rommel wrote to his wife in the usual honesty he addressed her with updating her with his conditions. He confesses to her that he has been in the barren desert for so long he is not sure of the date or his location and he has simply been attacking for days on end. Rommel out ran his supply lines and at one point was only able to keep going due to supplies seized from the British. The goal was to go from about Casa Blanca to Egypt and push the other off Africa.
Source: "The Rommel Papers", Erwin Rommel
Martin Blumenson "Field Marshal Erwin Rommel"
