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

Higher Spin Interacting Quantum Field Theory and Higher Order Conformal Invariant Lagrangians