  We introduce \emph{contact interactions hamiltonians} (self-adjointoperators
defined by boundary conditions) between $N$ massive particles in $R^3$, $N \geq
3$. We prove that they are limits (in strong resolvent sense) when $ \epsilon
\to 0$ of interaction through a two-body potential which scales according to $
V_\epsilon (|x|) =\epsilon ^{-3} V ( \frac {|x|}{ \epsilon} )$ where $ V(|x|) $
is an integrable function. The advantage of the formalism of contact
interactions is that the results do not depend on the shape of the
approximating potentials. Depending on the masses and symmetries there may be
three body bound states with wave function localized near the barycenter and
less localized four-body bound states. For some range of masses there is an
infinity of bound states with energies which accumulate geometrically to zero
(Efimov effect). For contact interactions these are all the bound states which
can be present in the $N$-body system. We study of zero range hamiltonians by
first compactly embedding the physical space $ L^2(R^{3 (N-1)}) $ in a larger
Hilbert space of more singular functions (Krein space) Estimates are done in
the auxiliary space, where strong resolvent convergence when $ \epsilon \to 0$
and spectral properties are easily established. If the hamiltonian \emph{in
Krein space} is positive, coming back to $L^2 (R^{3N})$ is done using the
compactness of the Krein map and the fact that for positive forms weak
convergence implies strong convergence. If it is not positive we use a somewhat
more sophisticated operation, $ \Gamma-$convergence [Dal]. In both cases the
limit operator is unique.
