We present lattice results for the spectrum of mesons containing one heavy
quark and of baryons containing one or two heavy quarks. The calculation is
done in the quenched approximation using the NRQCD formalism for the heavy
quark. We analyze the dependence of the mass splittings on both the heavy
and the light quark masses. Meson P-state fine structure and baryon hyperfi
ne splittings are resolved for the first time. We fix the b quark mass usin
g both M-B and M-Lambda b, and our best estimate is m(b)(<(MS)over bar>) (m
(b)(<(MS)over bar>)) = 4.35(10)((-3)(+2)) (20) Gev. The spectrum, obtained
by interpolation to m(b), is compared with the experimental data.