Can anyone recommend a book or reference material (written in English) that offers a gentle introduction to cyclotomic polynomials?
The book does not have to be too comprehensive.
I plan to apply the stuff I have learned from this book to undertake a more in-depth study of properties of odd perfect numbers.
I did study number theory in graduate school, but only up to the level of elementary number theory (using Burton).
You may take a look about the following references regarding the cyclotomic polynomial:
$(1)~~$ Number Theory in Science and Communication by Manfred R. Schroeder [Chapter 22, Page Number 232-246]
This book provides good examples and the topics are treated informally, stressing intuition rather than formal proofs.
$(2)~~$ Abstract Algebra by Paul Garrett [Chapter 8, Page Number 105-117]
This book proves many of the iconic basic facts about cyclotomic polynomials and cyclotomic fields.
$(3)~~$ Cyclotomic Polynomials by Brett Porter
$(4)~~$ The cyclotomic polynomials by G.J.O. Jameson
All the above references contains detail discussion with lot of examples. I think these may be helpful for understanding the subject. Good luck.