  We present the first fully microscopic, self-consistent, and self-contained
theory of superconducting weakly coupled periodic multilayers with tunnel
barriers in the presence of externally applied parallel magnetic fields, in the
local Ginzburg-Landau regime. We solve a nontrivial mathematical problem of a
microscopic derivation and exact minimization of the free-energy functional. In
the thin-layer limit that corresponds to the domain of validity of the
phenomenological Lawrence-Doniach model, our physical results strikingly
contrast with those of our predecessors. In particular, we completely revise
previous calculations of the lower critical field and refute the concept of a
triangular Josephson vortex lattice. We show that Josephson vortices penetrate
into all the barriers simultaneously and form peculiar structures that we term
''vortex planes''. We calculate the superheating field of the Meissner state
and predict hysteresis in the magnetization. In the vortex state, the
magnetization exhibits distinctive oscillatory behavior and jumps due to
successive penetration of the vortex planes. We prove that the vortex-plane
penetration and pinning by the edges of the sample cause the Fraunhofer pattern
of the critical Josephson current. We calculate the critical temperature and
the upper critical field of infinite (along the layers) multilayers. For finite
multilayers, we predict a series of first-order phase transitions to the normal
state and oscillations of the critical temperature versus the applied field.
Finally, we discuss some theoretical and experimental implications of the
obtained results.
  PACS numbers: 74.50.+r, 74.80.Dm
