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In English, prepositions are words like in, over, from, etc.

A preposition introduces a prepositional phrase. In the following examples, The highlighted phrases are the prepositional phrases.

He was sitting on the chair.

The man in the car is the driver.

In each prepositional phrase, there is an object of the preposition. In the first example, chair is the object of the preposition on. In the second example, car is the object of the preposition in.

In Greek, it is very important to learn what cases can be used with a given preposition, and to note what meaning is associated with the preposition for each case. Some prepositions consistently take only one case. Other prepositions may take two or three different cases, and have varying meanings depending on which case is used. You must associate the case and the meaning together when learning a preposition. For example, you should not be content to learn that ἐν means in. Rather you must learn that ἐν used with the dative case means in.

In Jn. 17:13, notice that κόσμῳ, the object of the preposition ἐν, is in the dative case:

I speak these things ἐν τῷ κόσμῳ

And of course, τῷ is dative because it must agree with the noun it modifies.

Learn the following prepositions, associating each case used with the corresponding meaning.

ἀπό	gen.	from	apostasy - a falling away from
ἄχρι	gen.	until, as far as
διά	acc.	on account of
	gen.	through	diameter - measure through
εἰς	acc.	unto, into
ἐκ, ἐξ preceding a vowel	gen.	out of	exit
ἐν	dat.	in
ἐνώπιον	gen.	before
ἔξω	gen.	outside [of]	exoskeleton - skeleton on the outside
ἕως	gen.	as far as, until
κατά	acc.	according to
	gen.	against, down from
μετά	acc.	after	metamorphosis - after form
	gen.	with
περί	acc.	around	perimeter - measure around
	gen.	concerning
πρό	gen.	before	program  - written before
πρός	acc.	to, toward	proselyte - one who comes to another religion
σύν	dat.	with
ὑπέρ	acc.	over, above	hyperactive - over active
	gen.	on behalf of
ὑπό	acc.	under	hypodermic - under the skin
	gen.	by

Many prepositions can be thought of geometrically, or spatially. Consider the prepositions represented in the graphic below, noting carefully the case with which the indicated meaning is associated.

This is an adaptation and simplification of a geometric representation of prepositions found on p. 80 in Lexical Aids for Students of New Testament Greek, by Bruce M. Metzger, 1977

Compounds of a preposition and a verb

Prepositions are often combined with verbs to form compound words. The effect of the preposition on the meaning of the verb varies, but we can loosely categorize most of these effects as follows:

1. The meaning of the preposition is combined with the meaning of the verb.
   For example βαίνω means I go. Remember that κατά can mean down. Accordingly, καταβαίνω means I go down.
   
   
2. The meaning of the verb is intensified. Compounds intensified by a prefixed preposition are sometimes called "perfectives" because the action is viewed as carried out to perfection, i.e. to completion. For example, ἐσθίω means eat, but when κατά is prefixed to form κατεσθίω, the meaning is devour  (See κατεσθίω used in Mk. 12:40.) Here, perhaps we see something reminiscent of an English idiom that makes the Greek seem less strange. If we talk about some one devouring his food, we may say he eats it up.
   
   
3. The meaning of the verb is unaffected. καλύπτω is cover. In a number of passages in the Septuagint (a Greek translation of the Old Testament scriptures), κατακαλύπτω means cover and is hardly, if at all, to be distinguished from καλύπτω.

Prepositions ending in vowels

Notice that the final vowel of κατά is dropped when the preposition is prefixed to ἐσθίω. The compound is κατεσθίω, not καταεσθίω. This will happen any time a preposition with a final vowel is prefixed to a verb beginning with a vowel, except in the cases of περί (for example, περί + αἰρέω = περιαιρέω) and πρό (for example, πρό + ἄγω = προάγω).

Repetition of the preposition

Often when a preposition is expressed as part of a compound verb, it is repeated in its own right.

ἐκβάλλει ἐκ τοῦ θησαυροῦ αὐτοῦ  Mt. 13:52
He brings out of his treasure

• to introduce cause, meaning because
• to introduce an object clause
• to introduce discourse, both direct and indirect