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Prepositions are such short words as 'in', 'of', 'to', 'about', 'with' etc. They are used to show the relationship of a noun to other words, or to the rest of the sentence. Their meaning is not always very strong, and their use often depends on the idioms of natural native English.
Prepositions form a closed set in English. (Sometimes the same word can be used with a noun, and also with a verb. In the first case it is a preposition; in the second it is a subordinating conjunction.)
As the name suggests, prepositions are usually placed (‘positioned’) in front of (‘pre’) the noun or noun phrase they apply to. (In academic English, this tendency is magnified: the ending of the last sentence is more formally written as "the noun or noun phrase to which they apply .") The NP (noun phrase) which follows a preposition is known as a prepositional complement.
Another convention of formal English is that if you use prepositions with a personal pronoun (or relative pronoun, it is correct to use the Objective form of the pronoun. "He gave it to me" feels natural; but some people become confused with – particularly – the preposition 'between'. "Between you and me" is correct; "between you and
I" is wrong.
Compound prepositions are two (or more) words usually used together. These include because of, out of.
Prepositions are often very confusing for foreign learners of English; furthermore they are one of the principal areas of difference between British and US English. They have very unclear meanings, and often a preposition in English may have several equivalents in the foreign language - and the other way round. The best way to study them is one by one - to learn the particular examples as they occur. There is good help in articles 436-441 of Practical English Usage.