What is the ruling on downloading PDF books from the internet for personal use, given that they are protected by copyright, and it is unknown whether the website has permission for electronic publication?

Downloading a book electronically differs from photocopying and reproducing it. If the download is for personal benefit and not for profit, and it is not known that the website owners have infringed upon the author's right, then there is no harm in downloading it and benefiting from it personally. Indeed, some scholars have permitted copying for personal need and seeking knowledge, provided it is not for profit.