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On October, 20, 1940 the Italian attack on Greece started.

On April, 06, 1941 the "German Reich" joined the "Balkan-Peninsula-Campaign" with an attack against Jugosalavia and Greece.
After surrender of the these two countries the strategically important Island of Crete was still defendend by 33000 troops from Great Britan, Australia and New-Zealand, as well as 10000 Greek soldiers.
On May, 20, 1941 a battle of unique historical importance for Crete began:
Solely Parachute- and Mountain Infantry-Troops were send into action by airtransport across the sea- in total 23500 German soldiers.
First objectives of the Parachute-Troops were the airfields of Malemes, Rethymnon and Heraklion, as well as the Capital Chania with the Souda-Bay. 
With numerous casualties in all places, they only succeeded in the occupation of the Malemes Airfield.
There, afterwards, the Mountain Infantry was landed , which with assistance of the Parachute Troops took the island after strong fights.
Introduction of further German Armed Forces by sea-transport was prevented by the Royal Navy.

The German losses were 6580 dead, woundet or missed in action.

More than 400 died out at sea.

Source: Memorial Tablet on the German War Cemetery at Malemes- May,20, 2001