〜について

について means "about" or "on the subject of": 日本の歴史について調べています, "I'm researching Japanese history". It's the everyday way to say what you're talking, thinking, writing or asking about.

Before another noun, add の: 環境問題についての本, "a book about environmental issues".

With は it picks out a topic, often to contrast it with others: その件については、後で連絡します, "as for that matter, I'll get back to you later".

It's neutral and works in speech and writing. The formal equivalent, common in business and official writing, is に関して. For "towards" someone, as in feelings or attitudes, use に対して instead.