We propose a self-contained description of Vasiliev higher-spin theories with the emphasis on nonlinear equations. The main sections are supplemented with some additional material, including introduction to gravity as a gauge theory; the review of th
e Fronsdal formulation of free higher-spin fields; Young diagrams and tensors as well as sections with advanced topics. The shortest route to Vasiliev equations covers 40 pages. The general discussion is dimension independent, while the essence of the Vasiliev formulation is discussed on the base of the four-dimensional higher-spin theory. Three-dimensional and $d$-dimensional higher-spin theories follow the same logic.
We derive the propagators for higher-spin master fields in anti-de Sitter space of arbitrary dimension. A method is developed to construct the propagators directly without solving any differential equations. The use of the ambient space, where AdS is
represented as a hyperboloid and its conformal boundary as a projective light-cone, simplifies the approach and makes a direct contact between boundary-to-bulk propagators and two-point functions of conserved currents.
We find exact spherically symmetric solution of 4d nonlinear bosonic higher-spin gauge theory, that preserves a quarter of supersymmetries of N=2 supersymmetric 4d higher-spin gauge theory. In the weak field regime it describes $AdS_4$ Schwarzschild
black hole in the spin two sector along with non-zero massless fields of all integer spins.
