Abstract The work is devoted to a wide class of formal groups, the ones given by polynomials, and to their relation to the Hilbert pairing. For the latter an explicit formula is obtained. The basic definitions are introduced in the work and the principal results are formulated, with the brief plans of proofs given for them. The detailed proofs are going to be given in the next work. © 2010 Allerton Press, Inc. References Honda, T. (1970) J. Math. Soc. Japan, 22 (1), pp. 213-246. Hazewinkel, M. (1978) Formal Groups and Applications, New York: Academic Bondarko, M.V., Vostokov, S.V. (2003) Proc. Steklov Inst. Math, 241, pp. 35-57. Vostokov, S.V. (1980) Math. USSR-Izvestiya, 15 (1), pp. 25-51. Fesenko, I., Vostokov, S.V. (1993) Local Fields and Their Extensions: A Constructive Approach, Providence, RI: Am. Math. Soc Kolyvagin, V.A. (1980) Math. USSR-Izvestiya, 15 (2), pp. 289-348. Shafarevich, I.R. (1950) Mat. Sb. (N.S.), 2 (68), pp. 113-146.