The Histories of Herodotus, whose primary medium of delivery was public recitation, were divided by Alexandrian editors into nine books, named after the nine Muses. For poet and "law-giver" Solon, the Muses were "the key to the good life"; since they brought both prosperity and friendship. Solon sought to perpetuate his political reforms by establishing recitations of his poetry—complete with invocations to his practical-minded Muses—by Athenian boys at festivals each year. He believed that the Muses would help inspire people to do their best. In literature
Ancient authors and their imitators invoke Muses when writing poetry, hymns or epic history. The invocation occurs near the beginning of their work. It asks for help or inspiration from the Muses, or simply invites the Muse to sing directly through the author. Originally, the invocation of the Muse was an indication that the speaker was working inside the poetic tradition, according to the established formulas. For example:

These things declare to me from the beginning, 
ye Muses who dwell in the house of Olympus, 
and tell me which of them first came to be. — Hesiod (c. 700 BCE), Theogony (Hugh G. Evelyn-White translation, 2015)

Sing to me of the man, Muse, the man of twists and turns
driven time and again off course, once he had plundered
the hallowed heights of Troy. —Homer (c. 700 - 600 BCE), in Book I of The Odyssey (Robert Fagles translation, 1996)
O Muse!
Here again, Calliope (epic poetry) carries a writing tablet; Clio (history) carries a scroll and books; Euterpe (song and elegiac poetry) carries a flute, the aulos; Erato (lyric poetry) is often seen with a lyre and a crown of roses; Melpomene (tragedy) is often seen with a tragic mask; Polyhymnia (sacred poetry) is often seen with a pensive expression; Terpsichore (choral dance and song) is often seen dancing and carrying a lyre; Thalia (comedy) is often seen with a comic mask; and Urania (astronomy) carries a pair of compasses and the celestial globe. Functions
In society
The Greek word mousa is a common noun as well as a type of goddess: it literally means art or poetry. According to Pindar, to "carry a mousa" is to excel in the arts. The word derives from the Indo-European root *men-, which is also the source of Greek Mnemosyne and mania, English mind, mental and monitor, Sanskrit mantra and Avestan Mazda. The Muses, therefore, were both the embodiments and sponsors of performed metrical speech: mousike (whence the English term music) was just "one of the arts of the Muses". Others included science, geography, mathematics, philosophy, and especially art, drama, and inspiration. In the archaic period, before the widespread availability of books (scrolls), this included nearly all of learning. The first Greek book on astronomy, by Thales, took the form of dactylic hexameters, as did many works of pre-Socratic philosophy. Both Plato and the Pythagoreans explicitly included philosophy as a sub-species of mousike.