I know there are many Muses, but it’s difficult to separate one from the pack and speak of that one specifically for any great length of time. The Muses tend to stay together as a group when spoken of in Greek myth.
In later society, each Muse was given a specific artistic domain, although in earlier traditions the Muses were not only fewer but less categorized into a given domain. The current “model,” which was decided on in the late Hellenistic period, gives each Muse her own domain of art and an emblem, which becomes that Muse’s attribute. Calliope holds a writing tablet, Clio holds scrolls, Erato plays the cithara, Euterpe plays the aulos, Melpomene wears or holds a tragic theater mask, Polyhymnia wears a veil, Terpsichore plays the lyre, Thalia holds or wears a comic theater mask, and Urania has with her a globe and compass.
As I said before, the Muses are usually referred to collectively when spoken of in myth, however there are some who are more involved and well-known than others. Calliope, for instance, was the mother of the famous Orpheus, and so she is involved in his mythology. Calliope was also supposed to be the intermediary in a dispute over Adonis between Aphrodite and Persephone. Clio brought the Phoenician alphabet to Greece and mother of Hyacinthus, lover of Apollo. Euterpe is said to have invented the double-flute. Terpsichore is said variously to be the mother of the Sirens by the river god Achelous and/or the mother of Linus by Apollo. Thalia and Melpomene are referenced often in theater as the goddesses of comedy and tragedy. Urania is also said to be the mother of Linus.
In early myth, there were originally only three Muses, as told by Pausanias to be Melete (“Practice”), Mneme (“Memory”), and Aeode (“Song”). Cicero added a fourth Muse, Telsiopes. Then a man named Pierus gave us the nine Muses we know today, who are sometimes said to be the names of his daughters, or that Pierus just made their names up. In one tradition the early three Muses were the daughters of Gaia and Uranus, but in the later tradition the Muses are said to be the children of Zeus and Mnemosyne.
The Muses are kindly figures, for the most part, who inspire mortals to be creative and artistic. But there are stories of mortals challenging the Muses, for example Thamyris, and when challenged the Muses can be as unforgiving and cruel as any of the other gods.
The Muses are said to inspire a great many things, things that we consider to be beautiful and pleasurable and good. Imagine a life without music, and what kind of life is that? The Muses appear to be kind, gentle, and wise mistresses of their respective domains.
On their Dark side, the Muses seem jealous and covetous of their skills. Yes, they inspire their mortal followers to be artistic, but the Muses aren’t actually giving the people these skills. Instead they are igniting the skill buried within the person and bringing it forward. The Muses, when challenged, seem to take this as a criticism of their skill, and affront to their very being, and respond in kind. They can be jealous of what they have, and harsh in their punishment, but luckily for everyone they are not jealous of what other people have.