  In the context of a strongly coupled Electroweak Symmetry Breaking, composite
triplet of heavy vectors belonging to the $SU(2)_{L+R}$ adjoint representation
and a composite scalar singlet under $SU(2)_{L+R}$ may arise from a new strong
interaction invariant under the global $SU(2)_L\times SU(2)_R$ symmetry, which
is spontaneously broken down to $SU(2)_{L+R}$. This thesis consists of two
parts. The first part is devoted to the study of the heavy composite vector
pair production at the LHC via Vector Boson Fusion and Drell-Yan annihilation
under the assumption that the interactions among these heavy vector states and
with the Standard Model gauge bosons are described by a $SU(2)_L\times
SU(2)_R/SU(2)_{L+R}$ Effective Chiral Lagrangian. The expected rates of
multi-lepton events from the decay of the composite vectors are also given. The
second part studies the associated production at the LHC of a composite vector
with a composite scalar by Vector Boson Fusion and Drell-Yan annihilation in
the framework of a $SU(2)_{L}\times SU(2)_{R}/SU(2)_{L+R}$ Effective Chiral
Lagrangian with massive spin one fields and one singlet light scalar. The
expected rates of same sign di-lepton and tri-lepton events from the decay of
the composite vector and composite scalar final state are computed. The
connection of the Effective Chiral Lagrangians with suitable gauge models is
elucidated.
