It's usually a topic on the first computer architecture class. It's a mid-of-the-book topic on most computer organization books, the classics like Hennesy Patterson or Tanenbaum have substancial portions dedicated to it. Both are books for a first course on computer architecture and design.
It's very important to understand it so that you can understand why sometimes pipelining is difficult or impossible.
Pipelining is done on basically every processor . It is like the laundry example you are not going to wait for dryer to finish before you load the washer. As soon as the clothes are done in the washer you will move them to the dryer and load the washer.
Our school introduced it in a year 2 computer organization course that was required for all CS majors. It went into how the processor converts assembly into instructions for the ALU, instruction pipelining, branch prediction (though only qualitatively), and the instruction and data cache, amongst other things.
We learned about in Computer Architecture (EECS 314).
We used the textbook "Computer Organization and Design" by David A Patterson and John L Hennessy. Branch Prediction comes up on page 341. I have it sitting on my desk here at work because it's such a useful book.
