Abstract: In this paper, various extensions of local fields are considered. For arbitrary finite extension K of the field of p-adic numbers, the maximum Abelian extension K^Ab/K and the corresponding Galois group can be described using the well-known Lubin–Tate theory. It is represented as a direct product of groups obtained using the maximum unramified extension of K and a fully ramified extension obtained using the roots of some endomorphisms of Lubin–Tate formal groups. We consider the so-called “generalized Lubin–Tate formal groups” and extensions obtained by adding the roots of their endomorphisms to the field under consideration. Using the fact that a correctly chosen generalized formal group coincides with the classical one over unramified finite extension T_m of degree m of field K, it was possible to obtain the Galois group of the extension (T_m)^Ab/K. The main result of the work, is an explicit description of the Galois group of the extension (K^ur)^Ab/K, where K^ur is the maximum unramified extension of K. Similar methods are also used to study ramified extensions of the field K.