From Flatland to Flatterland -- The third dimension -- Victoria's diary -- The visitation -- A hundred and one dimensions -- One and a quarter dimensions -- The topologist's tea-party -- Along the looking-glass -- Grape theory -- What is a geometry? -- Platterland -- Cat country -- The paradox twins -- The domain of the hawk king -- Down the wormhole -- What shape is the universe? -- No-branes and p-branes -- Flatterland -- The tenth dimension.