Here are some examples of N3-level grammar with their meanings:

〜ために (tame ni): In order to; for the purpose of Example: 日本語を勉強するために、毎日少し時間を取っています。(Nihongo o benkyou suru tame ni, mainichi sukoshi jikan o totteimasu.) – I take a little time every day to study Japanese.
〜てしまう (te shimau): Indicates completion of an action or regret Example: 宿題を忘れてしまった。(Shukudai o wasurete shimatta.) – I ended up forgetting my homework.
〜ものの (mono no): However; although; despite Example: 彼は日本語を勉強していますが、まだ上手ではありません。(Kare wa nihongo o benkyou shiteimasu ga, mada jouzu de wa arimasen.) – He is studying Japanese; however, he is still not very good at it.
〜てから (te kara): After; since Example: 仕事が終わってから、友達と食事に行きました。(Shigoto ga owatte kara, tomodachi to shokuji ni ikimashita.) – After work, I went out to eat with friends.
〜ということ (to iu koto): The fact that; the so-called Example: 彼は日本に行ったことがあるということです。(Kare wa Nihon ni itta koto ga aru to iu koto desu.) – He says he has been to Japan.
〜たり〜たりする (tari ~ tari suru): Doing things like ~; such as Example: 休みの日は、家で読書をしたり、友達と買い物に行ったりします。(Yasumi no hi wa, ie de dokusho o shitari, tomodachi to kaimono ni ittari shimasu.) – On days off, I do things like reading at home or going shopping with friends.
These grammar structures are commonly used in conversations and written texts at the N3 level in Japanese.