  We construct a graph complex calculating the integral ho- mology of the
bordered mapping class groups. We compute the ho- mology of the bordered
mapping class groups of various surfaces. Using the circle action on this graph
complex, we build a double complex and a spectral sequence converging to the
homology of the unbordered mapping class groups. We compute the homology of the
punctured mapping class groups associated to certain surfaces. Finally, we use
Miller's operad to get the first Kudo-Araki and Browder operations on our graph
complex. We also consider an unstable version of the higher
Kudo-Araki-Dyer-Lashoff operations.
