Abarim Publications' online Biblical Greek Dictionary
The prefix and preposition περι (peri) means "about". It implies both a circular motion and a motion out of or around some central point and often evokes a genitive case (out or around of). It survives in modern English in a vast array of words such as periscope (a thing with which to look around), periphony (surround sound) and the infinitely useful adjective and noun peripatetic, which describes a walking around, particular whilst following someone's teachings or the directions of one's vocation.
Our preposition is often joined with a verb that describes the conveying of information (to speak or talk about, teach about, hear about, know about) which leads to the subject assuming the genitive case. It may refer to cause, purpose or state of mind (getting upset about, being yelled at about, getting happy about, being concerned about, being compassionate about). It may introduce a topic of discourse (about this or that; concerning this or that).
Combined with the accusative case, our preposition describes the motion toward and arrival upon some location (like a city or a person), point of reason (like a conclusion or objection), or point in time (like tomorrow). Also with the accusative, our preposition may refer to some overall business which one is concerned about or busy with.
Our word is also deployed as part of a vast array of compound words, in which it usually carries the same meaning as when it is unbound, but may also declare a kind of circular boundary around the entire action of the other part of the compound: the whole of it, or very much.
Our prefix περι (peri) also comes with one pure derivation, namely the emphatic particle περ (per), which follows the secondary meaning of its unbound parent and means "very much" or "wholly so". In The New Testament this word does not occur in an unbound state but is in turn part of a small set of compounds.