Self-consistent evolutionary models were computed for our Sun, using Los Alamos interior opacities and Sharp molecular opacities, starting with contraction on the Hayashi track, and fitting the observed present solar L, R, and Z/X at the solar age. This resulted in presolar Y = 0.274 and Z = 0.01954, and in present solar 37Cl and 71Ga neutrino capture rates of 6.53 and 123 SNU, respectively.We explored the Sun's future. While on the hydrogen-burning main sequence, the Sun's luminosity grows from 0.7 Lsun, 4.5 Gyr ago, to 2.2 Lsun, 6.5 Gyr from now. A luminosity of 1.1 Lsun will be reached in 1.1 Gyr, and 1.4 Lsun in 3.5 Gyr; at these luminosities, Kasting predicts "moist greenhouse" and "runaway greenhouse" catastrophes, respectively, using a cloud-free climate model of the Earth; clouds could delay these catastrophes somewhat. As the Sun ascends the red giant branch (RGB), its convective envelope encompasses 75% of its mass (diluting remaining 7Li by two orders of magnitude; 4He is enhanced by 8%, 3He by a factor of 5.7, 13C by a factor of 3, and 14N by a factor of 1.5). The Sun eventually reaches a luminosity of 2300 Lsun and a radius of 170 Rsun on the RGB, shedding 0.275 Msun and engulfing the planet Mercury. After the horizontal branch stage (core helium burning), the Sun climbs the asymptotic giant branch (AGB), encountering four thermal pulses there; at the first thermal pulse, the Sun reaches its largest radial extent of 213 Rsun (0.99 AU), which is surprisingly close to Earth's present orbit. However, at this point the Sun's mass has been reduced to 0.591 Msun, and the orbits of Venus and Earth have moved out to 1.22 and 1.69 AU, respectively they both escape being engulfed. The Sun reaches a peak luminosity of 5200 Lsun at the fourth thermal pulse. It ends up as a white dwarf with a final mass of 0.541 Msun, shifting the orbits of the planets outward such that Venus and Earth end up at 1.34 and 1.85 AU, respectively. These events on the AGB are strongly mass-loss dependent; somewhat less mass loss can result in engulfment of Venus, or even Earth. Our preferred mass-loss rate was a Reimers wind with a mass-loss parameter η = 0.6 normalized from inferred mass loss in globular cluster stars. For reasonable mass-loss rates (0.8 > η > 0.4), the Sun's final white dwarf mass is between 0.51 and 0.58 Msun. The Sun spends 11 Gyr on the main sequence, 0.7 Gyr cooling toward the RGB, 0.6 Gyr ascending the RGB, 0.1 Gyr on the horizontal branch, 0.02 Gyr on the early AGB, 0.0004 Gyr on the thermally pulsing AGB, and 0.0001 Gyr on the traverse to the planetary nebula stage (the last three of these time scales depend sensitively on the amount of mass loss).