  We report extensive radial-velocity measurements of the two giant components
of the detached, 104-day period binary system of Capella. Our highly accurate
three-dimensional orbital solution based on all existing spectroscopic and
astrometric observations including our own yields much improved masses of 2.466
+/- 0.018 M_Sun and 2.443 +/- 0.013 M_Sun for the primary and secondary
(relative errors of 0.7% and 0.5%). Improved values are derived also for the
radii (11.87 +/- 0.56 R_Sun and 8.75 +/- 0.32 R_Sun), effective temperatures
(4920 +/- 70 K and 5680 +/- 70 K), and luminosities (79.5 +/- 4.8 L_Sun and
72.1 +/- 3.6 L_Sun). The distance is determined to be 13.042 +/- 0.028 pc.
Capella is unique among evolved stars in that, in addition to all of the above,
the chemical composition is known, including the overall metallicity [m/H], the
carbon isotope ratio 12C/13C for the primary, and the lithium abundance and C/N
ratios for both components. The latter three quantities are sensitive
diagnostics of evolution, and change drastically for giants as a result of the
deepening of the convective envelope during the first dredge-up. The secondary
is crossing the Hertzprung gap, while the primary is believed to be in the
longer-lived core-helium burning phase. However, we find that current stellar
evolution models are unable to match all of the observations for both
components at the same time, and at a single age, for any evolutionary state of
the primary. Similar problems are found when testing the rotational
synchronization, spin axis alignment, and orbital circularization of the system
against tidal theory. We conclude that our understanding of the advanced stages
of stellar evolution is still very incomplete. [Abridged]
