  The vector space of the tensors $\mathcal F$ of type (0,3) having the same
symmetries as the covariant derivative of the fundamental form of an almost
contact metric manifold is considered. A scheme of decomposition of $\mathcal
F$ into orthogonal components which are invariant under the action of
$U(n)\times 1$ is given. Using this decomposition there are found 12 natural
basic classes of almost contact metric manifolds. The classes of cosymplectic,
$\alpha$-Sasakian, $\alpha$-Kenmotsu, etc. manifolds fit nicely to these
considerations. On the other hand, many new interesting classes of almost
contact metric manifolds arise.
