Why use $\mu$-calculus and not LTL,CTL,CTL*?
As for a $\mu$-calculus formula not expressible in CTL*, see this post.

As for texts on the subject, you are likely to get further ahead by reading papers, as these topics are not covered in many books.
Still, the Handbook of Modal Logic may be a good start.

As for papers, try:

Expressive power of Temporal Logics

This PhD thesis

Emerson's Model checking and the Mu Calculus

And there are many more. Just google terms like "expressive power", "mu calculus" and "temporal logics".