  This thesis includes several original results. All of them are already
published or submitted for publication. I present here the short summary of
main results: The ultraviolet singular structure of the bulk-to-bulk
propagators for higher spin gauge fields in AdS4 space is analyzed in details.
One loop mass renormalization is studied on a simple example. The conformal
invariant Lagrangian with the k-th power of Laplacian for the hierarchy of
conformally coupled scalars with increasing scaling dimensions connected with
the k-th Euler density is rederived using the Fefferman-Graham ambient space
approach. The corresponding gauged ambient metric, Fefferman- Graham expansion
and extended Penrose-Brown-Henneaux transformations are proposed and analyzed.
Linearized gauge invariant interactions of scalar and general higher even spin
fields in the AdSD space are obtained. A generalized Weyl transformation is
proposed and the corresponding Weyl invariant action for cubic coupling of a
scalar to a spin \ell field is constructed. Using Noether's procedure several
cubic interactions between different HS gauge fields are derived, including
cubic selfinteraction of even spin gauge fields in a flat background. Then the
main result - the complete off-shell gauge invariant Lagrangian for the
trilinear interactions of Higher Spin Fields with arbitrary spins s1, s2, s3 in
a flat background is presented. All possibilities with different numbers of
derivatives are discussed. Restrictions on the number of derivatives are
obtained. For any possible number of derivatives this interaction is uniquely
fixed by gauge invariance up to partial integration and field redefinition.
Finally an off-shell generating function for all cubic interactions of Higher
Spin gauge fields is presented. It is written in a compact way, and turns out
to have a remarkable structure.
