TITLE: An introductory text on expanders
QUESTION [9 upvotes]: I am looking for a book that covers expander graphs rigorously. Preferably a book aimed at beginners.

REPLY [8 votes]: One should mention Lubotzky's lovely book "Discrete groups, expanding graphs and invariant measures" (1994), I think the first book written on the subject, which shows how the problem of constructing expander families connects to lots of other interesting mathematics.
My already-mentioned book with Giuliana Davidoff and Peter Sarnak was based on a master class I taught on the subject of Ramanujan graphs, itself based on a set of unpublished notes by Giuliana and Peter. Our aim is to present one family of expanders: the graphs of Lubotzky-Phillips-Sarnak (also constructed independently by Margulis). The prerequisites are those of a 2nd year master class: linear algebra, a standard course in algebra (groups, rings and fields), measure theory, some combinatorics.
The book "Expander families and Cayley graphs - a beginner's guide", by Mike Krebs and Anthony Shaheen (2011), starts lower in terms of prerequisites and has lots of drawings, tons of exercises, as well as students projects. Depending what kind of beginner you are, it may be more suitable...