وعليكم السلام 😃
"the book" is "al kitab"
the "ul" in "kitabul" belongs to the word " the teacher", it is actually "the".
in other words ,the sentence in Arabic is "book of the teacher" , no need to put "the" before "book".
the correct latin writing is "kitabu /a/lmuAlimi".
and the "u" in "kitabu" is for perfect in MSA, I mean if you want to speak the perfect MSA you need to end each word with Haraka, which is "a,u or i".