I will begin with the Muses, Apollo, and Zeus:
from the Muses and the skillful archer Apollo
come human bards and lyre players on earth,
and from Zeus, kings. Whoever the Muses love
is blessed: sweet sound flows from his mouth.
Rejoice, children of Zeus, and honor my song -
but I will remember you all and the rest of the song.
- Homeric Hymn 25
Generally refers to "The Twelve" but can refer to any of the many gods that are said to live atop Mt. Olympos, which is both a physical mountain (there is actually more than one mountain historically named Mt. Olympos) and a symbolic metaphor for where the gods live above the clouds. "The Twelve" varied from polis to polis, sometimes including Titans such as Kronos and Rhea or the Kharities (Graces) and Dionysos, but regardless of who was included there were normally still Twelve due to the sacredness of the number. "The Twelve" used here follows the Athenian canon, which is the most well known.
All gods and aspects may be worshiped, but it is tradition to differentiate between the Ouranic and Khthonic aspects as they have different ritual requirements. This traditionally means a seperation between Ouranic ritual with a preference for rituals to be done outside under the sky with partial offerings left on an altar raised off the ground, or Khthonic ritual with a preference for rituals to be performed in (sometimes) caves with whole offerings given to a small dug out pit.
For worship the Olympians are normally considered ouranic (of the sky/heaven) because they live on Mt. Olympos, however there are many Ouranic gods that are not Olympians, and some gods, including the Olympians, who have both Ouranic and Khthonic (of the earth/underworld) aspects, as is the case with Demeter and Zeus. The divide between ouranic and khthonic mostly applies to ritual and attempting to confine any given god solidly to either category is misguided. For this reason take the organization made here lightly as the gods are far more fluid in reality than being simply Ouranic or Khthonic.
King of gods and men, god of the sky, weather, fate, justice, and divine law. He is also a creation god, owing to his unfortunate portrayals in myth from a male-dominated society. In his creative capacity he is known as the rain-giver, cloud-gatherer, and loud-thunderer. He is married to Hera and is the father of many children, both divine and mortal, as most of the Olympian gods and many of the famed heroes are descended from him. His most essential myths often depicted in his temples are the myths of his birth and the Titanomachy. In iconography, he was typically depicted with an eagle, bull, or lightning bolt.
Queen of the gods, women, and marriage. Euripides names her as a goddess of the stars. She is Zeus' wife and confidant, her counsel honored by him, and she is afforded the same adoration as Zeus by the other Olympian gods. In later times she was worshiped as Zeus' equal. The Ancient Greeks worshiped her as a loving and noble goddess, highly respected and beloved (particularly among women), with several poleis claiming her presumed marriage site. Her most essential myths are the myths of her marriage, her involvement in The Illiad, and her persecution of Herakles. In iconography she is typically depicted with a cuckoo, peacock, hawk, lion, or scepter, and is usually crowned with a veil.
One of the original six children of Kronos, Poseidon received a third of the world and became the god of the sea, fishing, sailing, earthquakes, and creator of horses. He controls sea-faring weather, whether it is smooth sailing or disastrous storms, and, similar to Zeus, was a prolific lover with many children: gods, mortals, monsters, and animals alike. In myth he often plays a role in various city blessings. He helped build the impregnable walls of Troy (and wasn't paid for his work and Troy gained an eternal enemy), gifted Minos a sacred bull to prove his kingship, and competed against Athena to become the patron god of Athens. While he famously lost the patronship of Athens, their founding hero Theseus is said to be his son.
Perhaps owing to the ever-changing nature of water, in many myths he is a shape-shifting god, both changing his own form (as many gods do) as well as gifting the power to others. In one myth, the King Erysikhthon, cursed by famine, sold his daughter, Mestra, in marriage in order to use the bride-price to feed his eternal hunger. Mestra, however, was an unwilling bride and fled her husband to the sea begging the gods to save her. Poseidon came to her aid and gifted her his shape-shifting powers. She transformed into a man to escape her husband and returned to her father, but Eryskihthon sought only to abuse her power and continued to sell her off in marriage to continuously collect bride-prices. Each time, Mestra used her ability to transform into something new to escape her husbands until she finally found freedom after her father's hunger finally drove him to eat himself.
Goddess of Agriculture, particularly grain and corn. In myth she is attributed with teaching mortals how to grow food and so every meal is by her blessing. The Homeric Hymn to Demeter describes her most famous myth, the kidnapping of Persephone, which was significant to her wider cultus, the Eleusinian Mysteries. Of all the Mysteries, her cultus is the most well documented. An essential theme in her Homeric Hymn is the heartbreak of a grieving mother for her lost and symbolically dead child.
She and Persephone were commonly worshiped alongside each other and referred to as "the two goddesses". From the information surviving we know that their Mysteries revolved around theological concepts of the afterlife, death, and rebirth, deeply symbolic of her role in agriculture. It was said that initiates no longer feared death. In iconography she is typically depicted holding grain or a torch, alluding to her descent into Hades in search of Persephone. Crossed torches are used as a symbol for her Mysteries.
Virgin goddess of the Oikos, or the hearth, family, and home. In Athens and possibly other poleis she was believed to be the oldest of the Olympians, and in the Titanomachy she was said to be the first eaten by her father Kronos and the last to be spit back out when Zeus freed his siblings. Because of this she was traditionally honored "first and last" by the Ancient Athenians, receiving the first and last offerings during ritual. She had very few temples or sculptures in Ancient Greece, instead she was represented as the personification of the hearth (literally called a hestia) and presided over the hearth in every city, temple, home, and altar.
In Ancient Greece the hearth-flame was deeply significant. The most sacred flame in Greece was at Apollon's temple at Delphi, and it was said that every polis had their city-state hearth lit from the flame at Delphi, and in turn each household hearth was lit from its city-state hearth. It was considered ominous for the flame to extinguish. When new colonies were settled, the living hearth-flame was escorted with them to the new polis. In this way her flame can be thought of as the spiritual link between the gods and every worshiper, both past and present. There is not much information surviving about Hestia or household worship, and we have even less information about how she was worshiped outside of Athenian sources. She is often depicted veiled holding a flowered branch or kettle.
Virgin goddess of Wisdom, (strategic) warfare, and crafts such as pottery and weaving. Patron of Athens as well as many heroes. She was often depicted in a war helmet equipped with a spear and shield, sometimes accompanied by Nike (goddess of victory). She wielded the aegis, a shield made from the gorgon head of Medusa, an apotropaic symbol. In myth she is trusted by Zeus to bear his lightning bolts. Her most famous myths are of her birth, her involvement in The Illiad and The Odyssey, her competition with Poseidon for patronage of Athens, and her assistance of Herakles during his twelve labors, as well as many more.
The goddess of Love and Beauty. In Hesiod she emerges from the seafoam created from Ouranos' severed genitals and first graces the land of Cyprus as a Titan goddess, though in Homer she is a daughter of Zeus. In myth she is married to the smith-god Hephaestus, perhaps because jewelry was an important offering for her in Cyprus where her cultus first spread through Greece. However in Sparta she carries the epithet Aphrodite Areia as a goddess of war alongside Ares.
Philosophers liked to distinguish between two Aphrodites: Aphrodite Pandromos, the Aphrodite of pleasure, sexual desire, and the body; and Aphrodite Ourania who exemplifies the higher spiritual mode of Love and Beauty. In her Homeric Hymn it is said that when she stepped on the shores of Cyprus flowers sprouted beneath her feet, and indeed both the Kharities (also known as the Graces) and the goddesses of the Seasons are in her retinue. Her love of Adonis and her patronage of the Trojan prince Paris and Helen of Sparta are her most well-known myths. Her iconography usually includes doves, geese, apples, and roses, and in mythology she possesses a magic girdle which inspires intense desire. She is the beauty of nature and the soul, the love of friendship and family, as well as the love that spurs on generation. There is no aspect of the mortal world that Love or Beauty doesn't touch.
The god of war, conflict, and the battle-field, often depicted with his helm, shield, and sword. Like Zeus, he fathered many children. His divine children with Aphrodite include Deimos (Dread), Phobos (Fear), and Harmonia (Harmony), as well as the many Erotes (love gods). Ares is a defender of women and fathered the queen of the Amazons, fierce warrior women. In another myth his daughter, Alcippe, was assaulted on a beach and cried out for her father. Ares arrived in full splendor and smote the villian. He was celebrated in Arcadia under the epithet Gynaecothoenas, "feasted by women", given to him after the Spartans attempted to invade and were fought off by the city's women. Some of his sacred animals are vultures, venomous snakes, and dogs (associated with the carrion dogs of the battlefield).
The Messenger for the gods and the god of travel, trade, and shepherd's animals. He is typically depicted as a bearded man with a traveler's hat and cloak and the caduceus, the herald's staff. His most famous myth is the story of his birth where as a baby he snuck out of his cradle to steal and butcher Apollon's cattle, crafting the lyre along the way. When Apollo confronted him, he was impressed by his clever lies and the mesmerizing beauty of the lyre. In brotherhood, Apollon and Hermes exchanged gifts. Hermes gave Apollon his lyre, and Apollon in return gave Hermes divinatory arts. Hermes also served as guide to the dead in his role as psychopomp and is one of the few gods to be found on Mt. Olympos and in The Underworld. He was the one to go retrieve Persephone after her abduction and lead her out of the underworld, just as he guides our souls in. In this same role, he can also be prayed to for help with sleep and dreams.
Virgin goddess of the wilds and the hunt, goddess of childbirth and guardian of young girls and twin sister to Apollo. She is typically depicted as a young girl wearing a short chiton and wielding a bow and accompanied by animals. As one of the three virgin goddesses she is immune to Aphrodite's charms.
A virgin in Ancient Greece usually referred to an unwed women, which were typically young girls of only 13-14. Because of their age, and the desirability of chastity before marriage for secure family lines, this often came with the connotation that a "virgin" was chaste. Artemis' wild nature is symbolic for her maintained and unimpeachable autonomy. Unwed girls were also seen as wild creatures under her domain and in Athens all girls were required to serve as "Little Bears" in her temple for a year before they were allowed to marry. As a protector of young girls she oversees the pivotal transitions of a woman's life from birth, to puberty, to marriage and pregnancy.
In myth she is typically portrayed as a rather vengeful goddess punishing the men that encroached on her domain or person. The mythical explanation for why Athenian girls must serve as Little Bears is said to be because one of her sacred bears wandered into her temple one day and the Athenians killed it and so the tradition began as penance at the Pythia's direction. A man who spied her bathing was turned into a stag and torn apart by his hunting dogs. Such is the chaotic nature of the wilds. She is particularly associated with stags, bears, boars, and the moon, and she is said to be the patron of the hero Atalanta, the Amazonian huntress and symbol of the same strength and independence as the goddess.
God of music, harmony, enlightenment and guardian and protector of young boys. Like his sister he is also commonly depicted with a bow (but just as commonly with a lyre) and in later times was associated with the sun. Just as Artemis oversees the transitions in a woman's life, Apollo oversees the transitions in a man's from their initiation into their family, then the state, and finally the military. Because of this he was considered one of the ancestral gods of Athens as Apollo Patroos and had several festivals in his honor throughout the year.
As a god of music and harmony he is also considered leader of the Muses, the blessed goddesses who whisper and inspire the poets and indeed all artists to sing of the gods. He holds close associations to Hermes, as exemplified in the Homeric Hymn to Hermes, in which Hermes invents the lyre and gifts it to Apollo as payment for stealing his cattle. In later times, and perhaps as part of his association with light and enlightenment, he becomes associated with the sun just as Artemis was the moon.
His wide reaching fame, however, comes from his cultus in Delphi where his oracle, the Pythia, who was above reproach, spoke his word. His temple in Delphi was one of the oldest and longest lasting oracular cites of Ancient Greece and there are many stories both historical and mythologized of those seeking the divine wisdom of the Pythia. It was believed that Apollo only reigned in Delphi for half of the year, sharing the other half with Dionysos in the winter.
A god of crafts and craftsmen, a role he shares with Athena, as well as specifically stonemasonry, and smiths. He is also associated with fire in general, personified even, with his name literally translating as the word for fire in Homer. He is a disabled god, often depicted with an injured leg in pottery, an aspect significant in his role as a patron of craftsmen as craftsmen were in many cases injured and disabled, either as ex-soldiers or as a hazard of their crafts.
In the mythos almost any crafted item of significance was made by his hands, including the homes of the gods on Olympos, Achilles' famed armor, and even Pandora herself by Hesiod's cosmology. His most significant myth, in addition to the crafting of Achilles' armor and the sculpting of Pandora, is that of his asexual birth by Hera, said in some accounts to have been done in response to Zeus' asexual birth of Athena. It is said his forge resides in a volcano, and in iconography he is usually depicted with crafting tools astride a donkey or at his forge.
*Note: When researching this god, be aware that you will encounter many ableist slurs in reference to his disability.
The Golden Apple of Discord at the wedding of Peleus and Thetis, Jacob Jordaens, 1633 - Wikimedia Commons