Say what?! How do you pronounce all these crazy Greek names?!??
People (or in this case, gods and goddesses) become rulers (generally) one of three ways: appointment, usurption, or heir to the throne. According to Greek myth, all life descended from two beings: Gaia (the earth) and Uranus (the sky). From these two beings descended the twelve Titans, a group of gods and goddesses. Uranus didn't care much for his children so he imprisoned them in Tartarus (the Greek version of the underworld). One of his children finally overthrew him and imprisoned him; his name was Cronus.
Cronus married Rhea, another Titan but soon learned from his parents that his father's curse would fall upon him as well: one of his sons would overthrow him. In desperation, Cronus swallowed each of his children as they were born. Rhea finally wrapped a stone in a blanket after giving birth to Zeus and in this way, Zeus grew up and overthrew his father Cronus. He released all of his brothers and sisters, the Olympians, who later ruled the Greek heavens called Mount Olympus.
Although married to Hera, Zeus had many extra-marital relationships. In one myth, Zeus and his brother Poseidon both wanted to begin a physical relationship with a sea goddess named Thetis, but the other gods warned that a son born from Thetis would become greater than his father. Keeping in mind his unstable family history and thus heeding this warning, Zeus avoided Thetis and married her to a mortal, Peleus. source
No one wants 'rain on their wedding day.' So Zeus arranged for a wondrous ceremony, inviting everyone except Eris, the goddess of discontentment. Unwilling to forget Zeus's slight in leaving her out of the festivities, Eris rolled a golden apple among the guests with an inscription: for the fairest. Hera, (Zeus's wife and sister), Aphrodite, (Zeus's daughter and sometime lover), and Athena (Zeus's daughter) each desired the prize. Like any man wise enough to foresee the trouble this could bring, Zeus refused to get involved in the argument and appointed Paris, a mortal, to choose the winner of the golden apple. source
And like any woman who would stop at nothing to get what she wanted, each goddess resorted to bribing the human with wondrous gifts: Athena offered success in war and notoriety; Hera offered power and riches; and Aphrodite offered him the most beautiful woman on Earth. Needless to say, Paris chose Aphrodite and ultimately caused the downfall of one of the world's most powerful cities, Troy. The only problem: Helen was the most beautiful woman on Earth at the time. And she was also already married. source
Helen was married to Menalaus, king of Sparta, and brother to Agamemnon, king of Mycenae. Paris visited Menalaus with his cousin, Aeneas, and unsuspecting of Paris's plan, Menalaus welcomed the guests. Leaving for a funeral, Menalaus left Helen under the care of Paris for several days. During this time, Aphrodite caused Helen to fall in love with Paris and the two sailed off for Troy. Speculation about whether Helen was a willing participant still exists today. Nevertheless, she infamously became known as "the face which launched a thousand ships" and the cause of the Trojan War. source
Only desiring the best warriors and leaders, Menalaus and his brother Agamemnon sought out Odysseus, king of Ithaca and known for his prowess and cunning, and Achilles, known for his godly strength. Odysseus knew this war would last a very long time and only cause him trouble, so he avoided being recruited by acting like a madman. The ploy didn't fool the leaders and Odysseus joined the war effort to return Helen to Sparta. Achilles, donning the magical armour crafted by the god Hephaestus, willingly joined the war effort. Before leaving, Thetis, his mother, warned Achilles not to kill the son of Apollo, or else he would die by Apollo's hand. Achilles later does not heed his mother's warning. source
On their arrival at Troy, the Greeks sought a peaceful end to the problem and asked for Helen's return. The Trojans refused, thus starting the war which lasted ten long years. source
The Iliad takes place during the ninth year of the Trojan War. Over the years, the Greeks conquered many neighboring cities and took women as 'war prizes.' Agamemnon took Chryseis, the daughter of a Trojan priest of Apollo, and Achilles took Briseis. Ignoring the requests of her father, Agamemnon refused to give up his war prize. Chryseis's father appealed to Apollo for help, and the god struck the Greeks with a powerful plague, wiping out hundreds of men. Finally, a soothsayer revealed the cause of the plague, and Agamemnon reluctantly surrendered his war prize in exchange for Achilles's instead. This action caused Achilles to withdraw from the war effort and pray to his mother for help. Thetis asked for help from Zeus, and the god agreed to curse the Greeks for their actions against Achilles. Achilles's withdrawal from the war efforts devasted the men both physically and mentally. The Greeks had few successes. source
Seeing success on the Trojan side, Hector, a Trojan prince, offered sacrifices to Athena in thanks for her support but Athena refused the gifts, still sore about Paris choosing Aphrodite over her. source
Nestor, another Achian, finally tried to persuade Agamemnon to apologize to Achilles. The king agreed to return the war prize and also offered gold and riches; however, Achilles still would not accept. Agamemnon seriously considered abandoning the war and going home. A devastating day nearly ended everything when Agamemnon, Odysseus, and Diomedes, three strong Achian leaders, were severely wounded during a battle. Patroclus, a companion of Achilles, finally had enough. He approached Achilles and begged him to rejoin the war efforts. Achilles still refused, but allowed his companion to wear his golden armor and fight in his absence. source
The sight of the man they thought was Achilles renewed the Achians' spirits. Patroclus fought in Achilles absence and greatly helped the war effort. However, Apollo struck and stunned him and Hector took his life. Hector also took Achilles's golden armor off of Patroclus and wore it like a war prize. Angered and taking Athena's advice, Achilles scaled a wall on the battlefield and shouted three times; the sun shining against his body made him look like a god and spooked the Trojans, ending the battle for the day. In grief over his lost friend, Achilles rejoined the war effort, destined to kill Hector in single combat. source
Meanwhile, the gods and goddesses, involved in the war, began turning on each other. source
Achilles and Hector finally met on the battlefield. Hector said if Achilles should die, he would release his body and allow for a proper burial, asking that Achilles do the same. Achilles refused and fought the Trojan soldier, killing him. Achilles stripped the armor from Hector and drug his body from behind his chariot around the walls of Troy. Finally, he mourned the loss of his dear friend Patroclus for twelve days. source
Meanwhile, Priam, king of Troy, snuck into the Achian camp and begged for the release of his son, Hector's body. Heeding the requests of the gods, Achilles released the body and allowed Priam and Troy twelve days to mourn the loss of their leader. source
Toward the end of the war, Achilles suffered his fatal wound from Paris. Guided by the archer god Apollo, Paris shot an arrow and hit Achilles in the only spot not covered by the armor, his heel. The Achians built a great funeral pyre to honor their fallen hero, and his golden armor went to Odysseus. source
It was Odysseus who devised the plan to build the great horse and offer it as a war prize to the Trojans. Odysseus and a select group of men would hide inside the horse and the rest would sail away in their ships, hiding behind a nearby island. The plan worked. Although soothsayers tried to warn the Trojans otherwise, the foolish ones dragged the wooden horse inside the city gates and celebrated their assumed victory. Odysseus and his men descended from the horse in the middle of the night and took the city by surprise. By early morning, Troy fell. Finally, the ten-year war came to an end. source