  We analyze the production of Higgs particles at the early stage of the CERN
large Hadron Collider with a 7 TeV center of mass energy (lHC). We first
consider the case of the Standard Model Higgs boson that is mainly produced in
the gluon-gluon fusion channel and to be detected in its decays into
electroweak gauge bosons, $gg\to H \to WW,ZZ,\gamma\gamma$. The production
cross sections at $\sqrt s=7$ TeV and the decay branching ratios, including all
relevant higher order QCD and electroweak corrections, are evaluated. An
emphasis is put on the various theoretical uncertainties that affect the
production rates: the significant uncertainties from scale variation and from
the parametrization of the parton distribution functions as well as the
uncertainties which arise due to the use of an effective field theory in the
calculation of the next-to-next-to-leading order corrections. The parametric
uncertainties stemming from the values of the strong coupling constant and the
heavy quark masses in the Higgs decay branching ratios, which turn out to be
non-negligible, are also discussed. The implications for different center of
mass energies of the proton collider, $\sqrt s=8$-10 TeV as well as for the
design energy $\sqrt s= 14$ TeV, are briefly summarized. We then discuss the
production of the neutral Higgs particles of the Minimal Supersymmetric
extension of the Standard Model in the two main channels: gluon-gluon and
bottom quark fusion leading to Higgs bosons which subsequently decay into tau
lepton or $b$-quark pairs, $gg, b\bar b \to {\rm Higgs} \to \tau^+\tau^-,b\bar
b$. The Higgs production cross sections at the $\lhc$ and the decay branching
ratios are analyzed. The associated theoretical uncertainties are found to be
rather large and will have a significant impact on the parameter space of the
model that can be probed.
