〜つつ・〜つつも
while (doing); although
Verb ます-stem + つつ / つつも
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つつ is a written, literary version of ながら, with the same two meanings.
While: two actions by the same person at once: 音楽を聴きつつ、勉強する, "I study while listening to music". 周りの意見を聞きつつ、計画を進める.
Although, usually as つつも: 体に悪いと知りつつも、つい食べてしまう, "even though I know it's bad for me, I can't help eating it". The first half is often 知る, 思う or わかる, admitting you know better.
It attaches to the ます-stem. Don't confuse it with つつある (N3), "in the process of". In conversation, ながら is far more natural; つつ belongs in essays, speeches and fiction.
Examples
音楽を聴きつつ、勉強する。
I study while listening to music.
体に悪いと知りつつも、つい食べてしまう。
Even though I know it's bad for me, I can't help eating it.
景色を楽しみつつ、歩いた。
I walked along, enjoying the scenery.
悪いと思いつつも、約束を破ってしまった。
Although I knew it was wrong, I broke my promise.
周りの意見を聞きつつ、計画を進める。
We'll move the plan forward while listening to people's views.