January 2:
- 366 – The Alamanni, an alliance of west Germanic tribes, crossed the frozen Rhine in large numbers to invade the Roman Empire.
- 533 – Mercurius became Pope John II, the first pope to adopt a regnal name upon elevation to the papacy.
- 1492 – The Reconquista: The Catholic Monarchs, Queen Isabella I of Castile and King Ferdinand II of Aragon, expelled Abu 'abd-Allah Muhammad XII of Granada, the last of the Moorish rulers, from the Iberian Peninsula.
- 1942 – In the largest espionage case in United States history, 33 members of a German spy ring led by former South African Boer soldier and adventurer Fritz Joubert Duquesne (pictured) were convicted by the Federal Bureau of Investigation.
- 1959 – The Soviet spacecraft Luna 1 (illustrated by model), the first spacecraft to reach the vicinity of the Moon, was launched by the Vostok rocket from the Baikonur Cosmodrome near Tyuratam, Kazakh SSR.
More events: January 1 – January 2 – January 3
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