Higher-spin gauge theories is a rich and well-developed subject nowadays . As was shown by Fradkin and Vasiliev , all the no-go theorems that forbid interacting theories with fields of spin greater than two can be avoided for non-zero cosmological constant. In Diploma we review the main steps that lead from free higher-spin fields to Vasiliev equations . First , we review the Fronsdal equations in Minkowski and anti-de sitter backgrounds . Then we show how the usual metric formulation of gravity needs to be extended with vielbein and spin-connection as to introduce fields of half-integer spin . Analogously , instead of Fronsdal fields one can introduce the higher-spin analogs of vielbein and spin-connection . We then show how to write the equations for free fields of any spin in the unfolded form , where the symmetries are manifest . Also , we show that there exists an infinite-dimensional algebra , the higher-spin algebra , that the new variables are the gauge fields for . We end up with the Vasiliev equations that allow one to systematically derive nonlinear corrections to the higher-spin equations of motion .