We report on measurements of B differential cross sections and
correlated bb-bar cross sections in ppbar collisions at sqrt s = 1.8 TeV with
the Collider Detector at Fermilab (CDF).  We have also measured the ratios of
the branching fractions of B mesons decaying to a J/psi and a light meson and
b quark fragmentation fractions.  The Lambda_b baryon production has been
observed using the decays Labmda_b -> Lambda^+_c e^- nu-bar_c chi and
Lambda_b -> J/psi Lambda.