  We study asymptotic distribution of eigenvalues of the Laplacian on a bounded
domain in $ \R^n$. Our main results include an explicit remainder estimate in
the Weyl formula for the Dirichlet Laplacian on an arbitrary bounded domain,
sufficient conditions for the validity of the Weyl formula for the Neumann
Laplacian on a domain with continuous boundary in terms of smoothness of the
boundary and a remainder estimate in this formula. In particular, we show that
the Weyl formula holds true for the Neumann Laplacian on a $
\Lip_\alpha$-domain whenever $ (d-1)/\alpha<d $, prove that the remainder in
this formula is $ O(\lambda^{(d-1)/\alpha}) $ and give an example where the
remainder estimate $ O(\lambda^{(d-1)/\alpha}) $ is order sharp. We use a new
version of variational technique which does not require the extension theorem.
