HAMLET. That it should come to this!
But two months dead! Nay, not so much, not two;
So excellent a king, that was, to this,
Hyperion to a satyr ...

O God! a beast that wants discourse of reason
Would have mourn'd longer—married with my uncle,
My father's brother, but no more like my father
Than I to Hercules.
(1.2.140–143, 153–156)

In his first soliloquy, in act 1, scene 2, Hamlet compares his recently deceased father to Hyperion and his uncle, Claudius, who is newly married to his mother, to a satyr.

In Greek mythology, Hyperion—meaning ”The High One"—was one of the twelve Titans who ruled the world during the Golden Age of man, before the Olympians overthrew them. Hyperion was the Lord of the Light and the father of the sun, the moon, and the dawn.

A satyr was a small, male woodland spirit with the ears and tail of a horse or a donkey, who reveled in wine and dancing and who had an insatiable lust for women. Satyrs were said to have a unique ability to play musical instruments in such a haunting way that it compelled others, especially women, to follow them and join them in their drunken, animalistic debauchery.

Hamlet's comparison of his uncle Claudius to a satyr seems apt, in that Hamlet believes that Claudius, too, is a drunken, lustful creature who led his mother astray.

Near the end of the soliloquy, Hamlet makes a comparison between his father and his uncle by comparing himself to Hercules, the heroic Roman demi-god, son of Zeus, who was famous for his tremendous strength.

HAMLET. Look here upon this picture, and on this,
The counterfeit presentment of two brothers.
See what a grace was seated on this brow;
Hyperion's curls; the front of Jove himself;
An eye like Mars, to threaten and command;
A station like the herald Mercury
New lighted on a heaven-kissing hill:
A combination and a form indeed
Where every god did seem to set his seal
To give the world assurance of a man. (3.4.59–68)

In act 3, scene 4, the scene with his mother after the performance of "The Murder of Gonzago," Hamlet again compares his father to the Greek god Hyperion, and also compares him to the Roman gods Jove (or Jupiter, the king of the gods), Mars (son of Jove and the god of war), and Mercury (the wing-footed messenger of the gods). To Hamlet, his father was everything that a man should be.

HAMLET. Look you now what follows.
Here is your husband, like a mildew'd ear
Blasting his wholesome brother. Have you eyes?
Could you on this fair mountain leave to feed,
And batten on this Moor? (3.4.69–74)

Compared to the god-like man who was Hamlet's father, Claudius is nothing more than a rotten, mildewed ear of corn, contaminating the healthy ears of corn nearby.

Hamlet asks his mother how she could forsake her life on the mountaintop with Hamlet's father to live in the depths of a swamp with Claudius.