His father was a historian and advocate for Reverence for Life as expressed by Albert Schweitzer.

Hans had two brothers, Guenther and Wilfred, and sister Hiltgunt, who wrote an autobiography in 1974.

Inspired by Artin, Zassenhaus wrote a textbook Lehrbuch der Gruppentheorie that was later translated as Theory of Groups.

According to his sister Hiltgunt, Hans was "called up as a research scientist at a weather station"[1]: 55  for his part in the German war effort.

The following year he joined the faculty of McGill University where the endowments of Peter Redpath financed a professorship.

In 1959 Zassenhaus began teaching at University of Notre Dame and became director of its computing center in 1964.

The mathematics department was led by Arnold Ross; Zassenhaus found a home there until his retirement in 1982.