  In this paper, we construct multi-scalar, multi-center $p$-brane solutions in
toroidally compactified M-theory. We use these solutions to show that all
supersymmetric $p$-branes can be viewed as bound states of certain basic
building blocks, namely $p$-branes that preserve $1/2$ of the supersymmetry. We
also explore the M-theory interpretation of $p$-branes in lower dimensions. We
show that all the supersymmetric $p$-branes can be viewed as intersections of
M-branes or boosted M-branes in $D=11$.
