  We construct a set of reference frames for description of the orbital and
rotational motion of the Moon. We use a scalar-tensor theory of gravity
depending on two parameters of the parametrized post-Newtonian (PPN) formalism
and utilize the concepts of the relativistic resolutions on reference frames
adopted by the International Astronomical Union in 2000. We assume that the
solar system is isolated and space-time is asymptotically flat. The primary
reference frame has the origin at the solar-system barycenter (SSB) and spatial
axes are going to infinity. The SSB frame is not rotating with respect to
distant quasars. The secondary reference frame has the origin at the Earth-Moon
barycenter (EMB). The EMB frame is local with its spatial axes spreading out to
the orbits of Venus and Mars and not rotating dynamically in the sense that
both the Coriolis and centripetal forces acting on a free-falling test
particle, moving with respect to the EMB frame, are excluded. Two other local
frames, the geocentric (GRF) and the selenocentric (SRF) frames, have the
origin at the center of mass of the Earth and Moon respectively. They are both
introduced in order to connect the coordinate description of the lunar motion,
observer on the Earth, and a retro-reflector on the Moon to the observable
quantities which are the proper time and the laser-ranging distance. We solve
the gravity field equations and find the metric tensor and the scalar field in
all frames. We also derive the post-Newtonian coordinate transformations
between the frames and analyze the residual gauge freedom of the solutions of
the field equations. We discuss the gravitomagnetic effects in the barycentric
equations of the motion of the Moon and argue that they are beyond the current
accuracy of lunar laser ranging (LLR) observations.
