  We consider a Schr\"odinger operator $H=-\Delta+V(\vec x)$ in dimension two
with a quasi-periodic potential $V(\vec x)$. We prove that the absolutely
continuous spectrum of $H$ contains a semiaxis and there is a family of
generalized eigenfunctions at every point of this semiaxis with the following
properties. First, the eigenfunctions are close to plane waves $e^{i\langle
\vec \varkappa,\vec x\rangle}$ at the high energy region. Second, the
isoenergetic curves in the space of momenta $\vec \varkappa$ corresponding to
these eigenfunctions have a form of slightly distorted circles with holes
(Cantor type structure). A new method of multiscale analysis in the momentum
space is developed to prove these results.
  The result is based on the previous paper [1] on quasiperiodic polyharmonic
operator $(-\Delta)^l+V(\vec x)$, $l>1$. We address here technical
complications arising in the case $l=1$. However, this text is self-contained
and can be read without familiarity with [1].
