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We introduce \emph{contact (zero range) interactions } , a special class ofself-adjoint extensions of the N-body Schr\"odinger free hamiltonian $ H_0$restricted to functions with support away from the \emph{contact manifold} $\Gamma \equiv \cup \Gamma_{i,j} \;\;\; \Gamma_{i,j}\equiv \{x_i = x_j \; i\not= j \} \;,\; x_i \in R^3 $.  These extensions are defined by boundary conditions at $ \Gamma$.  We discuss the spectral properties as function of the masses and thestatistics  The (Efimov) spectrum is entirely due "conspiracy" of the contactinteractions of two pairs.  These states are called in Theoretical Physics \emph{trimers} if the twopairs have an element in common, \emph{quadrimers} otherwise.  The analysis can be extended to the case in which there is a regular two-bodypotential, but then the spectral properties cannot be given explicitly.  We prove that these interactions are limit (in strong resolvent sense) when $\epsilon \to 0$ of N-body hamiltonians $ H_\epsilon = H_0+ \sum_{i,j} \frac{1}{\epsilon^3}V_{i,j}( \frac {|x_i-x_j|}{\epsilon}) ,\; V_{i,j} \in L^1 $.  The result is \emph{ independent of the shape of the potential}  Strong resolvent convergence implies convergence of spectra.This makescontact interaction a valuable tool in the study of the spectrum of a system of$N$ particles interacting through potentials of very short range.

Zero range (contact) interactions conspire to produce Efimov trimers and quadrimers