  We introduce a notion of density which extends both the notion of Lelong
number and the theory of intersection for positive closed currents on Kaehler
manifolds. For arbitrary finite family of positive closed currents on a compact
Kaehler manifold we construct cohomology classes which represent their
intersection even when a phenomenon of excess dimension occurs. An example is
the case of two algebraic varieties whose intersection has dimension larger
than the expected number. The theory allows to solve problems in complex
dynamics. Basic calculus on the density of currents is established.
