The known sub-classes for Entity Events are:

Sub-Classes	Sub-Classes	Sub-Classes
CreatureSpawnEvent	CreeperPowerEvent	EntityChangeBlockEvent
EntityCombustEvent	EntityCreatePortalEvent	EntityDamageEvent
EntityDeathEvent	EntityExplodeEvent	EntityInteractEvent
EntityPortalEnterEvent	EntityRegainHealthEvent	EntityShootBowEvent
EntityTameEvent	EntityTargetEvent	EntityTeleportEvent
EntityUnleashEvent	ExplosionPrimeEvent	FoodLevelChangeEvent
HorseJumpEvent	ItemDespawnEvent	ItemSpawnEvent
PigZapEvent	ProjectileHitEvent	ProjectileLaunchEvent
SheepDyeWoolEvent	SheepRegrowWoolEvent	SlimeSplitEvent

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In addition to this, all the sub-classes inherit the following methods:

Entity getEntity();            //Entity who is involved in this event
EntityType getEntityType();    //EntityType of the Entity involved in this event

The EntityDamage event is thrown when an Entity is damaged.

EntityDamageEvent

@EventHandler
public void onEntityDamage(EntityDamageEvent e) {
    DamageCause cause = e.getCause();    //Get the event DamageCause
    double rawDamage = e.getDamage();    //Returns the damage before any calculation
    double damageModified = e.getDamage(DamageModifier.X);     //Returns the damage that would be caused with the specified modifier
    double finalDamage = e.getFinalDamage();    //Gets the final damage of this event, with all the calculations included

    e.setCancelled(boolean x);    //If for any reasons you want the event to not happen, you can cancel it
    e.setDamage(double damage);    //You can change the full damage the event will cause
    e.setDamage(DamageModifier modifier, double damage);    //Changes the damage considering any possible modifier
}

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Most of the times, the EntityDamageEvent will not be used. Instead, one of it's subclasses will be used, such as EntityDamageByEntityEvent or EntityDamageByBlockEvent. Both can be seen below.

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EntityDamageByEntityEvent

@EventHandler
public void onEntityDamageByEntity(EntityDamageByEntityEvent e) {
    //Retrieving the Entity that dealt damage
    Entity damageDealer = e.getDamager();

    //Retrieving the Entity that took damage
    Entity damageTaker = e.getEntity();

    //Retrieving the cause of the damage
    DamageCause cause = e.getDamageCause();

    //damage is the double value of the damage before all the resistances and modifiers have been applied
    double damage = e.getDamage();

    //FinalDamage is the double value of the damage after all the resistances and modifiers have been applied
    double finalDamage = e.getFinalDamage();

   //You can also set the raw damage (before modifiers) for the event to a different value
   e.setDamage(20.0);
}

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EntityDamageByBlockEvent

A simple extension to the EntityDamageEvent, but with one different method:

Block b = event.getDamager();    //Returns the block that dealt damage to the entity