読ませて

make/let (someone) read

→ 読む
読ま Irrealis stem + make or let someone do + Te-form (conjunctive)
verb · imperative Rare #33,404
make/let (someone) read Causative form of 読む, in the て-form; often used in requests such as “please let me read.”
JA: 私にその手紙を読ませてください。
EN: Please let me read that letter.
Conjugation of 読む

前回記事読ませてもらった

I read your previous article too.

— 甘い生活 (1960)

あなたが済んだらその新聞を僕に読ませて下さい

When you're done, please let me read that newspaper.

連絡しようとまず読ませてくれないか

Could you let me read it first before trying to contact them?

— エリート・スクワッド ブラジル特殊部隊BOPE (2010)

新しい本本当に大喜びで読ませていただきました

I was absolutely delighted to read your new book.