  The spectral curve is the key ingredient in the modern theory of classical
integrable systems. We develop a construction of the ``quantum spectral curve''
and argue that it takes the analogous structural and unifying role on the
quantum level also. In the simplest, but essential case the ``quantum spectral
curve'' is given by the formula "det"(L(z)-dz) [Talalaev04] (hep-th/0404153).
As an easy application of our constructions we obtain the following: quite a
universal receipt to define quantum commuting hamiltonians from the classical
ones, in particular an explicit description of a maximal commutative subalgebra
in U(gl(n)[t])/t^N and in U(\g[t^{-1}])\otimes U(t\g[t]); its relation with the
center on the of the affine algebra; an explicit formula for the center
generators and a conjecture on W-algebra generators; a receipt to obtain the
q-deformation of these results; the simple and explicit construction of the
Langlands correspondence; the relation between the ``quantum spectral curve''
and the Knizhnik-Zamolodchikov equation; new generalizations of the
KZ-equation; the conjecture on rationality of the solutions of the KZ-equation
for special values of level. In the simplest cases we observe the coincidence
of the ``quantum spectral curve'' and the so-called Baxter equation. Connection
with the KZ-equation offers a new powerful way to construct the Baxter's
Q-operator.
