  With their origin in thermodynamics and symbolic dynamics, Gibbs measures are
crucial tools to study the ergodic theory of the geodesic flow on negatively
curved manifolds. We develop a framework (through Patterson-Sullivan densities)
allowing us to get rid of compactness assumptions on the manifold, and prove
many existence, uniqueness and finiteness results of Gibbs measures. We give
many applications, to the Variational Principle, the counting and
equidistribution of orbit points and periods, the unique ergodicity of the
strong unstable foliation and the classification of Gibbs densities on some
Riemannian covers.
