Books on Mu-Calculus
An excellent book is Rudiments of $\mu$-calculus. It's not cheap though. You'd be better of learning from survey articles such as 


Bradfield, Julian and Stirling, Colin. Modal mu-calculi. In: P. Blackburn, J. van Benthem and F. Wolter (eds.), The Handbook of Modal Logic pp. 721-756. Elsevier (2006) or
Bradfield, J. C. and Stirling, C. P. Modal logics and mu-calculi: an introduction. In Handbook of Process Algebra (eds. J. Bergstra, A. Ponse and S. Smolka) 293--330. Elsevier (2001).