  Critical fluctuations of wave functions and energy levels at the Anderson
transition are studied for the family of the critical power-law random banded
matrix ensembles. It is shown that the distribution functions of the inverse
participation ratios (IPR) $P_q$ are scale-invariant at the critical point,
with a power-law asymptotic tail. The IPR distribution, the multifractal
spectrum and the level statistics are calculated analytically in the limits of
weak and strong couplings, as well as numerically in the full range of
couplings.
