  We present the micro-photoluminescence ($\mu$PL) and micro-reflectance
contrast spectroscopy studies on thin films of MoSe2 with layer thicknesses
ranging from a monolayer (1L) up to 5L. The thickness dependent evolution of
the ground and excited state excitonic transitions taking place at various
points of the Brillouin zone is determined. Temperature activated energy shifts
and linewidth broadenings of the excitonic resonances in 1L, 2L and 3L flakes
are accounted for by using standard formalisms previously developed for
semiconductors. A peculiar shape of the optical response of the ground state
(A) exciton in monolayer MoSe2 is tentatively attributed to the appearance of
Fano-type resonance. Rather trivial and clearly decaying PL spectra of
monolayer MoSe2 with temperature confirm that the ground state exciton in this
material is optically bright in contrast to a dark exciton ground state in
monolayer WSe2.
