I've read many books over the years. Most have been "not much", but a few I often reread or use as references.
"Clarinet" by Jack Brymer - A well-written book by the late Principal clarinetist of the London Symphony and one of my favorite players. The book covers everything from the development of the clarinet to performance practice to alternate fingerings. My most-read clarinet book.
"Heroes and Heroines of Clarinettistry" by Pamela Weston - A selective history of clarinetists and composers for the clarinet.
"From Where I Sit" by Jack Brymer - An engaging autobiography covering his life from the beginning of his clarinet days through his life as a professional clarinetist. Extremely readable, so much so that non-players would enjoy it.
"Haynes Clarinet Manual" by Stephen Howard - The best book for non-technical types on basic clarinet maintenance and repair that I've found. Just enough detail
"A Dictionary for the Modern Clarinetist" by Jane Ellsworth - One of a kind and comprehensive. Fun to browse, too.
"The Clarinet" - Eric Hoeprich - Similar to Brymer's, but with a scope beyond the classical clarinet. Very expensive, but maybe you can get it through library loan.