This report is a summary of the evidence for top quark production in
p p-bar collisions at a center of mass energy of 1.8 TeV which was
obtained by the CDF collaboration earlier this year.  The data
analyzed corresponds to an integrated luminosity of 19.3 pb**-1, recorded
with the CDF Detector at the Fermilab Tevatron Collider during 1992-1993.
Three different search channels for t t-bar production are used.
A search for dilepton events find 2 events, while two different methods
of identifying b-quark jets in events with W+>=3 jets finds 6 and 7 events,
respectively.  The probability that the observed total yield is
consistent with the estimated background of 5.96+0.49-0.44 is 0.26%.
Though the statistics are too limited to firmly establish the existence
of the top quark, a natural interpretation of the excess is that it is
due to t t-bar production.  Under this assumption, constrained mass fitting
of a subset of events yields a top quark mass of 174+-10+13-12 GeV/c**2
and a t t-bar production cross-section of 13.9+6.1-4.5 pb.