  Our aim in this work is to study a system of equations which generalises at
the same time the vortex equations of Yang-Mills-Higgs theory and the
holomorphicity equation in Gromov theory of pseudoholomorphic curves. We extend
some results and definitions from both theories to a common setting. We
introduce a functional generalising Yang-Mills-Higgs functional, whose minima
coincide with the solutions to our equations. We prove a Hitchin-Kobayashi
correspondence allowing to study the solutions of the equations in the Kaehler
case. We give a structure of smooth manifold to the set of (gauge equivalence
classes of) solutions to (a perturbation of) the equations (the so-called
moduli space). We give a compactification of the moduli space, generalising
Gromov's compactification of the moduli of holomorphic curves. Finally, we use
the moduli space to define (under certain conditions) invariants of compact
symplectic manifolds with a Hamiltonian almost free action of S^1. These
invariants generalise Gromov-Witten invariants.
  This is the author's Ph.D. Thesis. A chapter of it is contained in the paper
math.DG/9901076. After submitting his thesis in April 1999, the author knew
that K. Cieliebak, A. R. Gaio and D. Salamon had also arrived (from a different
point of view) at the same equations, and had developed a very similar
programme (see math.SG/9909122).
