We report on the status of b quark and b hadron production using
110 pb^-1 of data collected by the CDF detector between 1992 and 1995.  We
present the first direct measurement of the ratio of b quark cross sections at
sqrt s = 630 GeV and sqrt s = 1800 GeV, and an update on the measurement of
the B meson differential cross section.  We also present measurements of the
branching fraction for Lambda_b -> J/psi Lambda, and the product of
fragmentation fraction and branching fractions for the semileptonic decay
Lambda_b -> Lambda_c^+ e^- nu-bar X.