Cats are territorial animals and they may fight to defend their territory from other cats.
Cats may fight to establish dominance over each other.
Cats will often hiss at each other when they are feeling threatened.
Growling is another sign that a cat is feeling threatened or aggressive.
Cats may swat at each other with their paws.
Cats may pull at each other's fur if they are fighting.
If you are introducing two new cats to each other, it is important to do so slowly and carefully.