The battles in Animal Farm are the rebellion, the Battle of the Cowshed and the Battle of the Windmill.  The revolution begins when Jones is drunk and does not feed the animals for days.  The animals break into the shed to get food, and the men find them and attack them with whips.  The hungry animals, filled with revolutionary fervor by Old Major's dream speech, fight back.  They drive the men off.  That was the rebellion battle.

The Battle of the Cowshed occurs when Jones and some other farmers try to take back the farm.  The animals organize themselves and fight the men off, but a sheep dies and Snowball is wounded.  The animals are thrilled that they won, and local farmers start to accept Animal Farm's new ownership.

Men begin to trade with Animal Farm, but soon it causes problems.  Some farmers try to take advantage of the inexperienced animals.  Frederick pays them with counterfeit money and he and a group of men come and attack the windmill.  The animals fight back, but the windmill is destroyed.  This becomes known as the Battle of the Windmill.