###Hitler's Aggression

showed other countries that Hitler was aggressive and therefore in their best interest to join the allies?

Hitler had already shown that he was aggressive through conquering most of Europe, initially diplomatically and then militarily. His promise to the German people was to undo the perceived injustices of the Treaty of Versailles and make Germany Great again, and he did so through improving the German economy from its state of hyperinflation etc. and reducing unemployment, among other things.

By 1939, when the war broke out, Hitler had already won the Plebiscite in the Saarland (1935), remilitarised the Rhineland (1936), Anschlussed Austria (1938), annexed the Sudetenland (1938), and annexed the remainder of Czechoslovakia (1939). By August 1939 he was threatening Poland with war if they did not cede Danzig to the Reich. This, as well as Hitler's open expansion of the Wehrmacht and other branches of the armed forces in flagrant violation of the terms of the Treaty of Versailles, showed the world that Hitler was aggressive and a warmonger even before the Second World War broke out. This is why France and Britain promised to come to the Poles' aid in the event of a German invasion - they decided that appeasement of Hitler would stop there, as he was getting out of control. Hitler did not expect the British to honour their guarantee of the Poles, and so he invaded on the 1st of September 1939, sparking off the Second World War in Europe.

The Afrika Korps, the German forces sent to North Africa to help the Italians fight the British forces there, arrived in North Africa in March 1941, and Operation Barbarossa began on the 22nd of June 1941. By this time Hitler had conquered Poland, the Netherlands, Belgium, Luxembourg, France, Denmark, Norway, Yugoslavia, and Greece, and the Axis powers in Europe consisted of Germany, Italy, Hungary, and Romania. Hitler was already considered more than aggressive across the world; it was no concern of his at the time of Operation Barbarossa that the world would see him as aggressive.

###The Afrika Korps

Sadly, I have no particularly specialised sources on the Mediterranean Theatre apart from Fortress Malta (which does not concentrate on the Desert War, and rather on the Island of Malta which has relevance to the war but is not in Africa itself), so I will answer to the best of my ability based on related specialised sources, more general sources about the Second World War, and personal knowledge gained due to a personal interest in the Mediterranean theatre due to personal heritage and having lived there.

The Afrika Korps was sent to support Germany's Italian allies on the North African Front, where the Latin Army had been fighting the British forces here across the Egyptian and Libyan Deserts since Italy joined the war in June 1940. The Italians were not at all famed for good fighting quality, and their soldiers often had bad morale and training. Therefore, Hitler decided to send troops to North Africa to support and prop up the Italians. This was not a major deduction from the Wehrmacht's resources, because initially the Afrika Korps only consisted of part of a Panzer division, and it took until May, over 6 weeks after the initial landings, until Rommel had two divisions, the 5. Leichte Division and the 15th Panzer Division, still a very small portion of the Wehrmacht, considering this consisted of less than 50,000 men, a comparatively small portion of the over 7 million men serving in the German Armed Forces at this time. Therefore, by propping up the Italian Army and with the potential of taking the Middle Eastern Oil Fields, this minor investment could be well worth it for OKH.

###Barbarossa

Saying 'send troops to attack... Russia' does not do justice to the attack on the Soviet Union, Operation Barbarossa, in its huge scale. It was not simply a side project as that makes it sound, but a huge part of Hitler's Manifesto and ideals, and on its own possibly the most immense and deadly conflicts ever fought in terms of numbers.

Operation Barbarossa was Hitler's brainchild in his ideological desire to invade and destroy the Soviet Union, with him seeing Communism as the mortal enemy of Fascism and Nazi Germany, and therefore the manifestation of Communism in the Soviet Union was his mortal enemy. He aimed to destroy the Soviet state, and transform it into Lebensraum, living space, for the German people. He saw the slavs as untermenschen, under humans, that would be reduced to almost a race of slaves for German masters. This racial hatred indoctrinated into the German people through propaganda and the like would fuel the Eastern front into easily most brutal and awful front of the war, with the term Rassenkrieg, race war, very relevant here.

The invasion of the Soviet Union on the 22nd of June 1941 included a total of around 4 million men, 3 million of them in the Wehrmacht, along a 1800km front. I could go on for thousands of words on the invasion but I don't have the time for that! Instead I would recommend you watch this video on the losses sustained by soldiers and civilians of various nations in WW2, which shows you the immense scale and losses on the Eastern Front: http://www.fallen.io/ww2/ - This video is well worth a watch and is truly incredible at demonstrating the immense suffering and scale of WW2.

I would also say there are various immensely interesting books on the subject, that will go into far more detail than I ever could here, which are well worth reading.

However, the point is that when Germany invaded the Soviet Union, the Reich had few other distractions to divert its forces away from for Barbarossa; Britain stood alone against the might of the Axis, the rest of Europe under Fascist control, and America has not yet been drawn into the war. It was the ultimate culmination of Hitler's plans, and therefore a better wording would be that any other front would be a distraction from the Eastern Front, not the Eastern Front a distraction from them.

I hope I've answered your question, and I would be happy to answer any further inquiries to the best of my abilities.

Sources:

Stalingrad - Antony Beevor

The Second World War - Antony Beevor

Stalin: The Court of the Red Tsar - Simon Sebag Montefiore

Fortress Malta - James Holland