Jack Mathis created a great two volume set for them called REPUBLIC CONFIDIENTIAL that's like the other big books on the other studios. Volume 1, expensive and hard to find is on the history of the studio, its films, executives, buildings, and genres. Volume 2 is all about the stars, with contract information and a list of credits for performers.
Actually, Jack's books are much more interesting than those other coffee table catalogs. Mathis was involved with Republic for years and had access to production records, etc. I highly recommend these two volumes.
Of course, for serial fans there are VALLEY OF THE CLIFFHANGERS (or as we owners know it, VALLEY OF THE LAPBENDERS) and the VALLEY OF THE CLIFFHANGERS Supplement.