Prepositions show the relations between nouns or verbs and other words or phrases in the sentence; they often express locations in space or time. Some common prepositions are about, above, across, after, against, along, among, around, as, at, before, behind, below, beneath, beside, between, beyond, by, down, during, except, for, from, in, inside, into, like, near, of, off, on, onto, out, outside, over, past, regarding, since, through, throughout, till, toward, under, until, up, upon, with, within, and without.
Astrophysicists of the early 20th century, not knowing about nuclear processes, computed that a sun powered by chemical burning or gravitational shrinking could shine only for a few million years.
--"The Earth's Elements," Scientific American
Be careful to choose the preposition that reflects your intended meaning.
Some words or idioms specify exactly which preposition is preferred with the word or idiom. With these words or phrases, use the preposition that goes with the word, regardless of the usual meaning of the preposition.
In general, do not capitalize prepositions used in titles. See Capitalization.