  Fundamentals of the local smooth loops due to Sabinin are concisely outlined
together with the corresponding infinitesimal objects, so-called
\nu-hyperalgebras, and the analogue of the Lie groups theory. We apply here
this theory to to formulation of a new concept of loop of boosts. A
quaternionic model of the three-parametric loop of boosts is obtained and a
remarkable connection with geodesic loops of Lobachevskii space is found. A
description of Thomas precession in the light of general theory of smooth loops
is given.
