The Twenty First Century

"The Technic Civilization series...begins in the twenty-first century, with recovery from a violent period of global unrest known as the Chaos. New space technologies ease Earth's demand for resources and energy permitting exploration of the Solar system."

Sandra Miesel, Chronology of Technic Civilization IN Poul Anderson, The Van Rijn Method, New York, 2012, p. 611.

Only one story, "The Saturn Game," (pp. 1-73) is set in the twenty first century and it describes exploration of the outer Solar System by fleets of spaceships although it also reveals that there is an Apollo University in a city called Leyburg on Luna, the Moon, in 2057. (Willy Ley was a real world pioneer of space exploration.)

Mirkheim reveals further that, in the twenty first century:

space habitats called the O'Neill colonies were constructed in Lunar orbit sixty degrees ahead of or behind the Moon, at the Lagrangian points;
whole new industries flourished within the colonies;
such industries revived free enterprise;
this revival thoroughly transformed economics, thought and life;
meanwhile, diverse Terrestrial societies merged;
the economic, social revival and the cultural merging together generated a new, "Technic," civilization.

In the twenty second century, a further change occurred, faster than light interstellar travel.