Typhon

Typhon is the last known and most powerful child of the earth goddess Gaea, and is also known as the "Storm Giant" or "Father of all Monsters." His wife is Echidna and his father is the Protogenoi Tartarus. He is especially hated by Aeolus, because when he is defeated, thousands of Venti are released, thus making the master of the winds' job vastly more difficult. He is the single most powerful foe the Olympians have ever faced.

History
Thousands of years ago, after the First Olympian War, Gaea was enraged at the defeat of the Titans (her children), and of how they were locked away in Tartarus. She attempted revenge by sending her last and most powerful child, the great monster Typhon to destroy the Olympians. Typhon alone is the greatest foe the gods ever faced, even mightier than the Titans themselves.

Having never anticipated such a rival, the gods were quickly forced on the defensive and they eventually went into hiding, except for Zeus, who went into battle with his lightning. Zeus struck Typhon square in the chest with the tremendously powerful Master Bolt at point blank range, greatly weakening him. Zeus subsequently hurled Mount Etna on top of his foe, successfully trapping him. Ever since, Typon's raw power itself caused lava to ignite from the mountain's top in the form of a volcano. After the defeat of her most powerful child, Gaea admitted defeat and fell back to sleep, allowing the gods to rule Olympus without interference ever since.

Western Civilization
When the gods moved and followed the center of power of Western Civilization, Typhon was trapped in Mount Saint Helens. Like in Mount Etna, his raw power ignites lava from the mountain top. Though he was successfully imprisoned for thousands of years, his prison could not hold him forever.

The Titan's Curse
When hypothesizing about the identity of the "Bane of Olympus", Chiron suggests it might be Typhon, due to the latter being the most feared monster at Olympus, though Chiron considered it unlikely. It is later revealed to be the Ophiotaurus instead.

The Battle of the Labyrinth
Typhon is mentioned by Hephaestus. Later, during his efforts to kill a gang of Telekhines in The Battle of the Labyrinth, Percy was forced to call on all of his power to escape Mount Saint Helens. It was this that weakened the seal on Typhon's prison and made the Father of All Monsters stir in his sleep.

The Last Olympian
Typhon escapes in a catastrophic explosion of Mount Saint Helens. Following his escape, Typhon heads to New York City. Using the Mist, Typhon is able to conceal his true form from the mortals and appears as a freak storm. The gods, or at the very least Artemis, Apollo, Athena, Hermes, Ares, Dionysus, Hephaestus, and Zeus, are unable defeat him as Poseidon was occupied defending his undersea kingdom from Oceanus and Hades, Demeter, and Persephone refused to fight.

Not even Zeus' Master bolt, the most powerful weapon ever created, is able to stop him, as shown when Percy, through a projection on Olympus, sees that Typhon merely stumbled backwards before continuing his way towards Olympus. Typhon also incapacitates Dionysus and Hephaestus along the way, smashing Dionysus deep into a mountain, and smashing Hephaestus out of the sky with enough force to create a new lake in West Virginia. While the Olympians are busy fending off Typhon, the Titans make their way to Olympus, which is defended by demigods.

Percy prays to his father Poseidon and asks him to leave his kingdom and come to help the Olympians defeat Typhon. His father agrees and reluctantly leaves his kingdom to assist the gods. When Typhon steps into the Hudson River, the call of the ocean is heard and Poseidon rides into battle along with Tyson and his brethren, the Cyclopes, as well as Briares. They chain the monster down, and Poseidon opens a tunnel to Tartarus, casting Typhon down. Once Typhon is defeated, a wave of Venti (storm spirits) is born, much to Aeolus' dismay.

The Lost Hero
Jason Grace, Piper McLean, and Leo Valdez go to Boreas to get help for their quest to save Hera. As the god explains the release of the storm spirits, he shows them a video image of the gods defeating Typhon with Poseidon's help.

Appearance
Typhon's true appearance is unknown, since in The Last Olympian, he is always seen to be surrounded by thunder clouds. Through the mist, Typhon appears to mortals as a massive freak storm and tornadoes that tear apart everything in their path. To demigods (who are immune or highly resistant to the Mist) he appears as a colossal shadowy figure composed of dark clouds. According to Percy, Typhon was gigantic enough to use the Empire State Building as a baseball bat, and had blisters the size of buildings, clawed hands the size of city blocks, and feet the size of Yankee Stadium.

In Percy Jackson's Greek Gods, Typhon is described as more or less humanoid from the waist up, but his legs were like the bodies of boa constrictors. On each hand, he had a hundred fingers tipped with serpent heads. He had massive leathery wings, long matted hair that smelled like volcanic smoke. Typhon is so fearsome, that even the Olympian gods themselves all fled from him in terror after first seeing him, except for Zeus.

If a demigod or mortal looks at him too long they risk going insane from trying to comprehend what they are looking at. Based on comments, he has some sort of structure to serve as legs, and clawed-like hand structures hands to attack his enemies. Percy also says that he could not identify the monster's face because it changes every second to an even more horrifying monster than the previous one.

Abilities
Since Typhon is the Father of All Monsters, he is one of the most powerful, if not the most powerful, beings in all of Greek mythology, and the greatest single foe the Olympians have ever faced. Typhon's power is of apocalyptic proportions, as he rivals the combined powers of most, if not all the major Olympian gods. He presumably has the standard powers of an Olympian, but far surpassing that of any individual one, even the Big Three. Without Poseidon's intervention, it is more than likely that Typhon would have ultimately overcome them. The full extent of his power, however, is unknown. Much like Zeus, Typhon can create storms of tremendous power, including tornadoes, storms, and possibly hurricanes. He has incalculable superhuman strength and durability, far surpassing that of any individual god, even the Big Three. Typhon was able to fight most of the major gods to a near standstill, withstanding all of their attacks throughout, including multiple attacks from the Master Bolt (which only made him stagger), numerous lesser thunderbolts, the arrows of Apollo and Artemis, as well as the Trident of Poseidon (which did, however, significantly injure him). He was strong enough to hit Hephaestus with enough force to create a new lake and smash Dionysus deep into a mountain. Even while trapped under Mount Etna, Typhon's raw power itself caused lava to ignite from the mountain's top in the form of a volcano.

Trivia

 * Typhon is often known as the most powerful monster of all, but Porphyrion has claimed that he and his fellow giants are the most powerful children of Gaea, which raises questions over who is more powerful.
 * Typhon is established as Gaea's most powerful child in Percy Jackson's Greek Gods. It is more than likely that Porphyrion was boasting, since he also claimed to be more powerful than Kronos.
 * In The Last Olympian, Hermes reveals that Typhon is the Olympians' greatest enemy, making Kronos the second greatest.
 * Interestingly, in Percy Jackson's Greek Gods, Percy mentions that since most of the Olympian gods fled from Typhon all the way to Egypt in the form of animals, they might have induced Egyptian myths about "gods with animal heads." However, Percy admits that this is unlikely, since Egyptian myths are much older than Greek ones.
 * In Percy Jackson's Greek Gods, Typhon is also called Typhoeus.