What were the three battles the allied powers fought during ww2?

The allies fought in scores or hundreds of battles in WW2. According to the dictionary, a battle is a hostile encounter or engagement between opposing military forces that might last days, weeks, or months. A 'front' is the part of the battle nearest the enemy. A theater of war is

the entire land, sea, and air area that is or may become involved directly in war operations (M-W online dictionary)