Is the Unix Programmers Manual relevant for Linux?

The Unix Programmers Manual you linked to is probably mostly relevant for Linux also. However, that manual was published in 1979. Things have changed since then in all descendants of the original Unix.

This is the collection of man pages for an antique version of Unix. There is little point in reading that: it is of historical interest only. Man page collection exist for your current version of Unix. You can read a man page with the man command, or in various online databases (Ubuntu, FreeBSD, etc.).

Don't try to read all the man pages. I have about 23000 man pages installed on my home computer… Man pages are reference documents, to be consulted when you need to know about one specific command or function. They are often incomprehensible if you don't know anything about that part of the system.

If you want to learn programming from a book, what you need is a book written to teach Unix programming. Advanced Programming in the UNIX Environment (APUE) is a classic; there are many others.