Let $X$ a dual Banach space (there exists a Banach space $Y$ such that $X=Y'$). 
A weak\* semigroup on $X$ is a semigroup $(T\_t)\_{\geq 0}$ on $X$ such that, for all $x\in X$, we have $T\_tx\to x$ in the weak\* topology when $t\to 0^+$.


I know a lot of books about $C\_0$-semigroups but not about weak\* semigroups.



> 
> Do you know a good place to read about weak\* semigroups and their generators? A book would be perfect. 
> 



Reference for weak*-semigroup
Echoing the remark of @Bill Johnson, one possibility is [van Neerven's book](http://books.google.hu/books/about/The_adjoint_of_a_semigroup_of_linear_ope.html?id=9jbvAAAAMAAJ&redir_esc=y) on adjoint semigroups. 


