  Now that the Higgs boson has been observed by the ATLAS and CMS experiments
at the LHC, the next important step would be to measure accurately its
properties to establish the details of the electroweak symmetry breaking
mechanism. Among the measurements which need to be performed, the determination
of the Higgs self-coupling in processes where the Higgs boson is produced in
pairs is of utmost importance. In this paper, we discuss the various processes
which allow for the measurement of the trilinear Higgs coupling: double Higgs
production in the gluon fusion, vector boson fusion, double Higgs-strahlung and
associated production with a top quark pair. We first evaluate the production
cross sections for these processes at the LHC with center-of-mass energies
ranging from the present $\sqrt s=8$ TeV to $\sqrt s=100$ TeV, and discuss
their sensitivity to the trilinear Higgs coupling. We include the various
higher order QCD radiative corrections, at next-to-leading order for gluon and
vector boson fusion and at next-to-next-to-leading order for associated double
Higgs production with a gauge boson. The theoretical uncertainties on these
cross sections are estimated. Finally, we discuss the various channels which
could allow for the detection of the double Higgs production signal at the LHC
and the accuracy on the self-coupling that could be ultimately achieved.
