読ませて

let (someone) read, allow (someone) to read

→ 読む
読ま Irrealis stem + せ Causative + て Te-form (conjunctive form)
verb Rare #40,589
let (someone) read, allow (someone) to read This is the て-form of the causative form of 読む. In these contexts, it means allowing someone to read.
JA: その本を読ませてください。
EN: Please let me read that book.
Conjugation of 読む

前回の記事も読ませてもらったよ

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.

新しい本を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.