  In this note we introduce primitive cohomology groups of locally conformal
symplectic manifolds $(M^{2n}, \omega, \theta)$. We study the relation between
the primitive cohomology groups and the Lichnerowicz-Novikov cohomology groups
of $(M^{2n}, \omega, \theta)$, using and extending the technique of spectral
sequences developed by Di Pietro and Vinogradov for symplectic manifolds. We
discuss related results by many peoples, e.g. Bouche, Lychagin, Rumin,
Tseng-Yau, in light of our spectral sequences. We calculate the primitive
cohomology groups of a $(2n+2)$-dimensional locally conformal symplectic
nilmanifold as well as those of a l.c.s. solvmanifold. We show that the l.c.s.
solvmanifold is a mapping torus of a contactomorphism, which is not isotopic to
the identity.
