について is a combination of the 格助詞(かくじょし) (case marking particle)
に, the verb う - Verb 就(つ)く ‘to assume a position’, and the 接続助詞(せつぞくじょし) (conjunction particle) て. It is most often translated as ‘about (A)’, or ‘concerning (A)’, with the literal translation being closer to ‘taking the position of (A)’, or ‘assuming the topic of (A)’.
について may be used after nouns, or noun-phrases (phrases that use こと, の, etc).
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彼女(かのじょ)と別(わか)れたことについて話(はな)したいんだけど時間(じかん)ある?
I want to talk to you about breaking up with my girlfriend, but do you have time?
契約(けいやく)のことについて、何(なに)か質問(しつもん)はありますか。
Assuming the topic of the contract, do you have any questions?
行(い)きたい国(くに)について、作文(さくぶん)を書(か)いてください。
Please write an essay about the country you want to visit.
について may also appear before の + noun. In this use, it means ‘(A) that is about (B)’.
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契約(けいやく)についてのパンフレットは明日(あした)届(とど)くので、しっかりとお読(よ)みになってください。
The brochure regarding the contract will be delivered tomorrow, so please make sure to read it.
今日(きょう)は和製(わせい)英語(えいご)についてのレッスンをしたいと思(おも)います。
Today, I am thinking of giving you a lesson about Wasei Eigo.
It is rare to see について actually using the kanji 就(つ). について itself is regularly considered as a single 連語(れんご) ‘compound word’, rather than a combination of its parts.