  We present an efficient diagrammatic method to describe nonlocal correlation
effects in lattice fermion Hubbard-like models, which is based on a change of
variables in the Grassmann path integrals. The new fermions are dual to the
original ones and correspond to weakly interacting quasiparticles in the case
of strong local correlations in the Hubbard model. The method starts with
dynamical mean-field theory as a zeroth-order approximation and includes
non-local effects in a perturbative way. In contrast to cluster approaches,
this method utilizes an exact transition to a dual set of variables. It
therefore becomes possible to treat the irreducible vertices of an effective
{\it single-impurity} problem as small parameters. This provides a very
efficient interpolation between band-like weak-coupling and atomic limits. The
method is illustrated on the two-dimensional Hubbard model. The
antiferromagnetic pseudogap, Fermi-arc formations, and non-Fermi-liquid effects
due to the van Hove singularity are correctly reproduced by the lowest-order
diagrams. Extremum properties of the dual fermion approach are discussed in
terms of the Feynman variational principle.
