Iterated Shimura integrals

In this paper, I continue the study of iterated integrals of modular forms and noncommutative modular symbols for $\Gamma\subset{\rm SL}(2,\mathbb Z)$ started in my paper math.NT/0502576. The main new results involve a description of the iterated Shimura cohomology and the image of the iterated Shimura cocycle class inside it. The concluding section of the paper contains a concise review of the classical modular symbols for ${\rm SL}(2)$ and a discussion of open problems.