Multiple intersections of D-branes and M-branes

We give a classification of all multiple intersections of D-branes in ten dimensions and M-branes in eleven dimensions that correspond to threshold BPS bound states. The residual supersymmetry of these composite branes is determined. By dimensional reduction composite p-branes in lower dimensions can be constructed. We emphasize in dimensions D ≥ 2 those solutions which involve a single scalar and depend on a single harmonic function. For these extremal branes we obtain the strength of the coupling between the scalar and the gauge field. In particular, we give a D-brane and M-brane interpretation of extreme p-branes in two, three and four dimensions.