Measurements of the top quark mass and the ttbar production cross section, obtained by CDF and D0 Collaborations at the Tevatron are presented. The methodology of analyses and their underlying assumptions are summarized. The CDF and D0 top mass averages, based on approximately 100 pb^-1 of data collected by each experiment in Run-I, and obtained from a set of selected measurements in several channels are M_t = 176.0 +/- 4.0(stat) +/- 5.1(syst) GeV/c^2 and M_t = 172.1 +/- 5.2(stat) +/- 4.9(syst) GeV/c^2, respectively. The combined Tevatron top quark mass is M_t = 174.3 +/- 3.2(stat) +/- 4.0(syst) GeV/c^2, where the correlations between CDF and D0 averages were taken into account. The CDF measurement of the tt-bar cross section (assuming M_t = 175 GeV/c^2) is sigma_tt = 7.6 +/- ^1.8 _1.5 pb, and the D0 value (assuming M_t = 172.1 GeV/c^2) is sigma_tt = 5.9 +/- 1.7 pb. In anticipation of the much increased statistics in Run-II, the fact that top quark physics is one of the best windows to new physics beyond the Standard Model is emphasized.