We note that current observational evidence strongly favors a conventional recombination of ionized matter subsequent to redshift z = 1200, followed by.reionization prior to redshift z = 5 and compute how this would have occurred in a standard scenario for the growth of structure. Extending prior semianalytic work, we show by direct, high-resolution numerical simulations (of a COBE normalized CDM + Λ model) that reheating will occur in the interval 20 > z > 7, followed by reionization and accompanied by a significant increase in the Jeans mass. However, the evolution of the Jeans mass does not significantly affect star formation in dense, self-shielded clumps of gas, which are detached from the thermal evolution of the rest of the universe. On average, the growth of the Jeans mass tracks the growth of the nonlinear mass scale, a result we suspect is due to nonlinear feedback effects. Cooling on molecular hydrogen leads to a burst of star formation prior to reheating, which produces Population Ⅲ stars with Ω_* reaching 10~(-55) and Z/Z_☉ reaching 10~(-3.7) by z ～ 14. Star formation subsequently slows down as molecular hydrogen is depleted by photodestruction and the rise of the temperature. At later times, z < 10, when the characteristic virial temperature of gas clumps reach 10~4 degrees, star formation increases again as hydrogen line cooling become efficient. Objects containing Population Ⅲ stars accrete mass with time and, as soon as they reach 10~4 K virial temperature, engage in renewed star formation and turn into normal Population Ⅱ objects having an old Population Ⅲ metal-poor component.
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