  As a main result of the paper, we construct and justify an asymptotic
approximation of Green's function in a domain with many small inclusions.
Periodicity of the array of inclusions is not required. We start with an
analysis of the Dirichlet problem for the Laplacian in such a domain to
illustrate a method of meso scale asymptotic approximations for solutions of
boundary value problems in multiply perforated domains. The asymptotic formula
obtained involves a linear combination of solutions to certain model problems
whose coefficients satisfy a linear algebraic system. The solvability of this
system is proved under weak geometrical assumptions, and both uniform and
energy estimates for the remainder term are derived.
  In the second part of the paper, the method is applied to derive an
asymptotic representation of the Green's function in the same perforated
domain. The important feature is the uniformity of the remainder estimate with
respect to the independent variables.
