Study of the classical (Newtonian) problem of the body of least resistance in various classes of bodies: non-convex axisymmetric and non-axisymmetric bodies (two- and three-dimensional cases, with and without restrictions imposed on the maximal number of collisions of particles with the body). Minimization of specific resistance of infinite surfaces. Minimization of resistance to bodies moving in a medium of positive temperature, herein including bodies which perform both translational and rotational motions, and of rotating bodies with rough surface. Relationship between the problem of minimal resistance of non-convex rotating bodies and the one-dimensional problem of mass transfer. Exactly solvable problems of mass transfer; relationship between linear transport and mass transfer problems. The problem of finding the pressure generated by a given non-parallel flux of particles and the inverse problem of determining density of the flux generating a given pressure distribution.