Listed below are different types of aggressive behaviors and possible solutions.

1. Play Aggression
Cats by nature love to attack, scratch, or bite anything that moves.  Play aggression is an extension of your cat's predatory nature. Although this type of aggression is most commons in kittens it can occur in cats of all ages.  The most commons forms of play aggression include, attacking hands and feet, pouncing on anyone who moves, and even inappropriate biting/scratching during play.

Solution
Do not encourage your kitten or cat in rough play, scratching, or biting.  Allowing him to do this reinforces inappropriate behavior and teaches him that this type of behavior is allowed.  If he tries to nip or scratch your hand, teach him that this behavior is not allowed. Disengage your hand by gently pushing toward him (if you try to pull away, he’ll hang on even more tightly).  Give him toys instead of your hand. Leave him alone for a few minutes.  Return after he has calmed down and try playing again using a proper toy. If he continues to grab your hand, say “NO” in a stern voice.  He’ll soon get the idea.

2. Over-Stimulation Aggression
This type of aggression occurs when a cat becomes overly excited while being pet.  It's actually normal behavior for cats to have quick reversals of mood and behavior. There's a fine line between enjoyable petting and irritating handling. Or you may have unknowingly touched a sensitive or painful area. Once the petting reaches a certain threshold, the cat will reject any further touching.

Solution
Watch your cat for signs of over stimulation.  These include: restlessness, twitching tail, turning her ears back, or your cat turning or moving her head toward your hand.  Once you see these signs it is time to stop petting your cat and let her go about her business. If you want to avoid the problem in the future you can watch the clock while you are petting your cat and get an idea of how long she will tolerate the affection and make sure you don't go beyond her threshold.  This along with paying attention to warning signs should eliminate this type of aggression.

3. Territorial Aggression
Cats are very territorial, much more so than other animals. Territorial aggression occurs when a cat feels that his territory has been invaded by an intruder. Cats defend territory from other animals, including humans, by driving them away with threats. Territorial problems often occur when a new cat is brought into a household, when a young kitten reaches maturity, or when a cat encounters neighborhood cats outside. It’s not uncommon for a cat to be territorially aggressive toward one cat in a family, and friendly and tolerant to another.

Solution
There are several steps you can take to help and stop this type of aggression.  First, don't try to punish the aggressive cat when he does this. Punishment is likely to elicit further aggression, which will only make the problem worse. Second,  do separate the cats when they fight. You can usually do this with distraction, making a loud noise, squirting the cats with water, or throwing something soft at them. Don't try to pull them apart.  Take the separated cats to separate rooms to calm down. You can also try to start the introduction process over again from the beginning. Slowly, letting the cats have contact with each other. Try giving each a towel or a toy that you rubbed on each cat (between their eye and ear) so they can get use to each other's scent. Another option to try is Feliway; it is a synthetic facial pheromone preparation that has a calming effect on cats by simulating a calm and friendly environment.

4. Defensive Aggression
This type of aggression is a result of fear, anger, or illness.  It occurs because the cat feels that it is threatened and cannot escape.  This can occur in response to punishment or the threat of punishment from a person, an attack or attempted attack from another cat, or any time he feels threatened or afraid. The cat becomes aggressive in an attempt to protect itself from the perceived danger, not in order to hurt you.

Solution
Again it is important to consult a vet if cat has suddenly become aggressive to check for signs of illness.  To solve this type of aggression simply remove whatever is frightening your cat and give your cat some time to calm down.  If your cat is fearful of strangers there are a few things you can do to help remedy this. First, don't let the stranger approach your cat.  Wait for your cat to come near the stranger, who should be sitting quietly and waiting for the cat to approach.  This may take a long time.   But until your cat approaches on his own terms, and finds that nothing bad happens, he will not develop his own confidence to trust people.

5. Redirected Aggression
This can occur when a cat becomes aroused or aggressive due to one stimulus such as the sight of a cat outdoors or a loud, disturbing noise and attacks a human or another animal that is nearby within their reach. Again the cat displays this aggression from a natural instinct to protect itself and its territory, it is not actually trying to hurt you. 

Solution
The first step you should take is trying to figure out what the cause of your cat's aggression is and remove it.  If the source of your cat's aggression is an outdoor cat close the curtains so your cat cannot see the other cat or shoo the stray out of your yard.  If your cat directs this aggression towards you, leave him alone until he has calmed down.  If the aggression is directed to another cat in the household, separate the two cats until the agitated cat is relaxed.  You can then reintroduce the two of them slowly. 

General Recommendations to reduce aggression

• If your cat's behavior changes suddenly, consult a veterinarian to rule out illness or injury.
• Spay or neuter your cat.  Intact males are much more likely to fight than neutered males.
• Never punish the cats involved.  Punishment is likely to elicit further aggression and fearful responses.
• Try a synthetic pheromone preparation such as Feliway, which has a calming effect on cats. 
• Consult an expert - Cat aggression can be a serious problem. If you feel that things are getting out of control, consult your veterinarian and ask her to refer you to a local cat behavior expert
• In extreme cases, consult with your veterinarian about medicating your cats while you're working on a behavior-modification program. Your veterinarian is the only person who is licensed and qualified to prescribe medication for your cat, so don't attempt to give your cat any over-the-counter or prescription medication without some guidance.