  In this paper we obtain multifractal generalizations of classical results by
L\'evy and Khintchin in metrical Diophantine approximations and measure theory
of continued fractions. We give a complete multifractal analysis for
Stern--Brocot intervals, for continued fractions and for certain Diophantine
growth rates. In particular, we give detailed discussions of two multifractal
spectra closely related to the Farey map and the Gauss map.
