  We report on Raman experiments performed on a single crystal MoTe$_2$ sample.
The system belongs to the wide family of Transition Metal Dichalcogenides which
includes several of the most interesting two dimensional materials for both
basic and applied physics. Measurements were performed in the standard basal
plane configuration, by placing the $ab$ plane of the crystal perpendicular to
the wave vector $k_i$ of the incident beam to explore the in plane vibrational
modes, and in the edge plane configuration with $k_i$ perpendicular to the
crystal $c$ axis, thus mainly exciting out-of-plane modes. For both
configurations we performed a polarization-dependent Raman study and we were
able to provide a complete assignment of the observed first- and second-order
Raman peaks fully exploiting the polarization selection rules. Present findings
are in complete agreement with previous first-order Raman data whereas a
thorough analysis of the second-order Raman bands, either in basal- or
edge-plane configurations, provides new information and a precise assignment of
these spectral structures. In particular, we have observed Raman active modes
of the $M$ point of the Brillouin zone previously predicted by ab-initio
calculations and ascribed to either combination or overtone but never
previously measured.
