  For several different boundary conditions (Dirichlet, Neumann, Robin), we
prove norm-resolvent convergence for the operator $-\Delta$ in the perforated
domain $\Omega\setminus \bigcup_{ i\in 2\varepsilon\mathbb Z^d
}B_{a_\varepsilon}(i),$ $a_\varepsilon\ll\varepsilon,$ to the limit operator
$-\Delta+\mu_{\iota}$ on $L^2(\Omega)$, where $\mu_\iota\in\mathbb C$ is a
constant depending on the choice of boundary conditions.
  This is an improvement of previous results [Cioranescu & Murat. A Strange
Term Coming From Nowhere, Progress in Nonlinear Differential Equations and
Their Applications, 31, (1997)], [S. Kaizu. The Robin Problems on Domains with
Many Tiny Holes. Pro c. Japan Acad., 61, Ser. A (1985)], which show strong
resolvent convergence. In particular, our result implies Hausdorff convergence
of the spectrum of the resolvent for the perforated domain problem.
