Here are some recommendations which could be useful.
The following books are playing presumably in the same league as W.W. Petersons Error-Correcting Codes from 1972 which was recommended by Antonios-Alexandros-Robotis.
You may check the table of contents of these books and you will see a wealth of information around error control coding with substantial chapters containing cyclic codes, resp. CRCs. I've consulted parts of each of them with benefit, especially with focus on CRCs.
Error Control Coding by S.Lin and D.J. Costello
The Theory of Error-Correcting Codes by F.J. MacWilliams and N.J.A. Sloane (founder of OEIS)
Coding and Information Theory by S. Roman
Some basic knowledge around finite fields is definitely helpful.
Finite Fields for Computer Scientists and Engineers by R.J. McEliece is a very nice, easy to read introductory book. It was so delightful, that I also bought The Theory of Information and Coding from him.
Introduction to finite fields and their applications by R. Lidl and H. Niederreiter is much more comprehensive and provides a thorough introduction to the theme.
Sometimes when I have to work with certain CRCs in my job, there are questions regarding the undetected error probability of certain codes. I could find helpful information in
Codes for Error Detection by Torleiv Klove.
Hint: You might also visit my answer to Error correcting codes in real life where I put some references to papers regarding CRCs and undetected error probability.