We derive the full canonical formulation of the bosonic sector of eleven-dimensional supergravity and explicitly present the constraint algebra. We then compactify M-theory on a warped product of homogeneous spaces of constant curvature and construct a minisuperspace of scale factors. First classical behaviour of the minisuperspace system is analysed and then a quantum theory is constructed. It turns out that there are similarities with the 'pre-big-bang' scenario in string theory.