You've come to this page because you've asked about English simple prepositions.
This is the Frequently Given Answer to such questions.
Goold Brown, writing in The Grammar of English Grammars (1858. New York:Samuel S. & William Wood) on page 439, states that "Grammarians differ considerably in their tables of the English prepositions.". What words are and are not simple prepositions (i.e. one-word prepositions, as opposed to complex prepositions that are multi-word phrases) depends from what grammarian is listing them. This is not helped by the fact that words have become, and continue to become, prepositions over the years and centuries, and words that were prepositions fall into desuetude.
William Chauncey Fowler in English Grammar: The English Language in Its Elements and Forms (1855. New York: Harper.) provides one of the few not-simply-alphabetical lists of English simple prepositions on page 370, categorizing and annotating them as follows:
Simple prepositions: [Fowler by "simple" here means etymologically simple, rather than one-word.] at, after (comparative of aft), by, down, for, from, in, of, on, over, past, round, since, till, to, through, under, up, with
Prepositions formed by prefixing a-: aboard, above, about (from Old English abutan), across, against (from Old English gean, from the verb gan "to go"), along, amid, amidst, among (from Old English onmang, from the verb gemengan "to mingle"), amongst, around, athwart
Prepositions formed by prefixing Old English be-: before (replacing the older afore and tofore), behind, below, beneath, beside, besides, between, betwixt, beyond
Prepositions formed by compounding two prepositions, or a preposition and an adverb: into, throughout, toward, towards, underneath, until, unto, upon, within (also inwith in older works), without (also outwith in older works)
Participles that became prepositions: bating, barring, concurring, during, excepting, notwithstanding, regarding, respecting, touching
Imperative verbs used as prepositions: save, except
Adjectives used as prepositions, implying a following to: nigh, near, next, opposite
Conjunctions used as prepositions: but
To those can be added several more. U.S. grammarian Josiah Swett (An English Grammar: Comprehending the Principles and Rules of the Language. 1844. New Hampshire: Claremont Manufacturing Company) and U.S. grammarian Peter Bullions (The Principles of English Grammar. 1850. New York: Pratt, Woodford) both add aslant and off. British grammarian William Lennie (The principles of English grammar. 1863. London: Routledge, Warne, & Routledge.) adds concerning and excepting. Modern grammarians add alongside, as, atop, despite, inside, like, nearby, and outside; various loanwords used as prepositions such as anti, versus, and vis-á-vis; as well as dialect-specific prepositions such as the Yorkshire English while (for until).
However, some grammarians also subtract. Lennie, for example, asserts that toward is not a preposition but "always an adjective, and means 'ready to do or learn'". (In part, this is a difference between British English, where towards is the preferred form, and United States English, where toward is the preferred form. Many British grammarians, like Lennie, have tried to create a distinction between the words in order to provide a justification for the dialectal difference. However, the Old English root is toweard, for which toweards is the adverbial genitive — a spelling that can even be found in a few 19th century texts.)
The largest point of difference, both between authorities and across time, is in the participles that have become prepositions. Swett disagreed with many grammarians that any of the aforementioned participles are prepositions, calling it (on page 80) "a liberty not warranted in the structure of our language". However, most dictionaries nowadays and most other grammarians (including Swett's contemporaries) recognize some, if not all, of them as prepositions. To the aforegiven are usually nowadays also added the following participles as prepositions: considering, excluding, failing, following, pending, and saving.
This indicates that forming prepositions from participles is a process that is still occurring, and the set of prepositions is not as closed and immutable as some would have it to be. Interestingly, most 21st century U.S. authorities now recognize, in addition to the existing ones ending in the Old English -ing, one participle ending in the Latin -ent as a preposition: absent.