1). Perseus was the son of Danae, the only child of Acrisius king of Argos. Disappointed by his lack of male heirs, he asked an oracle if this would change. The Oracle told him that one day he would be killed by his daughter's child. She was childless and, meaning to keep her so, he shut her up in a brazen chamber. But Zeus came to her in the form of rain, and impregnated her. Soon after, their child Perseus was born.
None too happy, but unwilling to provoke the wrath of the gods by killing his offspring, Acrisius cast the two into the sea in a wooden chest. They washed ashore on the island of Seriphos, where they were taken in by Dictys, the brother of king Polydectes, who raised the boy to manhood. Now after a time Polydectes fell in love with Danae, and so wanted to get Perseus out of the picture. He thereby hatched a plot to send him on a suicide mission.
Polydectes placed some strong hints that he would love to have the head of Medusa, one of the gorgons whose very expression turns people to stone. He then announced that he would woo Hippodamia and so needed the others to provide him with horses (a different myth). Shamed at having nothing to give, Perseus left to get him Medusa's head. This was of course not easy, and for a long time he wandered aimlessly, without hope of ever finding her or being able to accomplish his mission when he did.
The gods Hermes and Athena came to his rescue. They led him to the Phorcides, three perpetually old women with one eye and tooth between them and sisters of the gorgons. Perseus took the eye and would not return it until they had given him directions. He also received winged sandals, a magic wallet, the cap of Hades that made one invincible, an adamantine sickle, and a mirrored shield. With all this he came upon the sleeping gorgons. By viewing Medusa's reflection in his shield he could safely approach and cut off her head. The other two gorgons pursued him, but he became invisible and escaped.
On his way back, Perseus passed by Ethiopia, then ruled by a king Cepheus. At the time his daughter Andromeda had been abandoned to prevent the sea monster Cetus from destroying the country. Perseus used Medusa's head to kill the monster and rescue the girl in exchange for the promise of her hand; she was already betrothed to the king's brother Phineus, who thus plotted to kill Perseus, but a little more exhibition of the head fixed that. And on returning to Argos and discovering his mother had had to take refuge from the violent ways of Polydectes, he put a quick end to those too, and made Dictys king.
Perseus then returned his tools and gave Medusa's head as a gift to Athena. He started for Argos, but learning of the oracle instead went to Larissa, where athletic games were being held. By chance Acrisius was there, and Perseus accidentally struck him with his javelin, fulfilling the oracle. Too shamed to return to Argos he then gave the kingdom to Megapenthes son of Proetus (Acrisius' brother) and took over his kingdom of Tyrins, also founding Mycenae and Midea there.
Perseus and Andromeda had six sons: Perses, Alcaeus, Heleus, Mestor, Sthenelus, and Electryon. The first was supposedly left in Ethiopia and became ancestor of the emperors of Persia to explain the similarity of the country's name and Perseus'. His descendants ruled Mycenae to Eurystheus son of Sthenelus, after whom Atreus got the kingdom, and include the great hero Heracles son of Amphitryon son of Alcaeus.
2). Perseus is a northern constellation, representing the legendary slayer of Medusa. It is one of the 88 modern constellations, and was also one of the 48 listed by Ptolemy. It contains the famous variable star Algol (β Per), and is also the location of the radiant of the annual Perseid meteor shower.