Interpretatio graeca

Interpretatio graeca is a Latin term for the common tendency of ancient Greek writers to equate foreign divinities to members of their own pantheon. Herodotus, for example, refers to the ancient Egyptian gods Amon, Osiris and Ptah as "Zeus", "Dionysus" and "Hephaestus", respectively.

Roman version
The equivalent Roman practice was called interpretatio romana. The first use of this phrase was by Tacitus in his Germania (ch. 43), in which he reports on a sacred grove of the Naharvali, saying "Praesidet sacerdos muliebri ornatu, sed deos interpretatione Romana Castorem Pollucemque memorant" ('a priest presides in woman's dress, but in the interpretation of the Romans, they worship the gods Castor and Pollux'). Elsewhere (ch. 9) he says that the chief gods of the ancient Germans were Hercules and Mercury&mdash;referring to Thor and Odin respectively.

Rome assumes the Greek gods
Roman culture owed much to the ancient Greeks. The Etruscans had already incorporated some Greek gods and used a version of the Greek alphabet. The Greek colonies founded in southern Italy from the eighth century BCE contributed much to the young city, and later, when the Romans conquered the Hellenistic world, they adopted a new wave of Greek beliefs and practices. (See Romans and Greeks for details.) Where the two mythologies shared an origin, the interpretations came naturally; Zeus and Jupiter, for example, were both derived from Dyeus of the Proto-Indo-European pantheon. Elsewhere the fit was less precise, and the Roman god might add attributes borrowed from the Greek, but remain distinct: Mars retained his Latin association with agriculture and fertility alongside his warlike attributes and, quite unlike the fearsome Greek Ares, was a benevolent and widely-revered cult figure.

Some Di Indigetes (native Roman gods), such as Janus and Terminus, had no Greek equivalent and so retained an independent tradition; a few, like Bona Dea, did the same despite sharing attributes with a Greek figure (in this case Artemis). Others, like the twelve assistants of Ceres, became mere adjuncts to imported Greek deities (here Demeter).

Rome and the gods of the empire
The Romans interpreted Celtic and Near Eastern gods as Roman deities with equal facility. Cernunnos and Lugh were identified with Mercury, Nodens to Mars as healer and protector, Sulis to Minerva, and the Anatolian storm god with his double-headed axe became Jupiter Dolichenus, a favorite cult figure among soldiers.

Even the Jewish invocation of Yahweh Sabaoth may have been identified with Sabazius.

Where the Romans had no equivalent figure, they did not hesitate to add foreign deities to their pantheon. Sometimes they would change the name: when Cybele was adopted from the Phrygians (the Greeks had previously interpreted her as Rhea), she was called Magna Mater deorum Idaea. Sometimes they would not: Apollo was called Apollo in both Greek and Latin.

Greco-Roman equivalences
Roman mythology was strongly influenced by Greek mythology and Etruscan mythology. The following is a list of most credited cult equivalences between the respective systems. Note however that many mythographers dismiss both the equivalences made in ancient times and those proposed by modern scholars.

Interpretatio germanica
Interpretatio germanica is the practice of identifying Roman gods with the names of Germanic deities by the Germanic peoples. According to Rudolf Simek, this occurred around the 1st century CE when both cultures came into closer contact, and the only reliable insight into interpretatio germanica can be found in the Germanic translations of the Roman names for the days of the week: Simek states that the problematic nature of interpretatio germanica is evident, and that divine attributes appear to have been the obvious factors for the correspondence between Jupiter and Thor, but for the other figures one must rely on speculation, and that far too little is known about what role the gods played in then-contemporary belief to be able to use their identification with particular Roman gods to trace their roles in later Norse mythology.
 * The day of Mars is translated as the day of Ziu/Tyr (Tuesday).
 * The day of Mercury is translated as the day of Wodan/Odin (Wednesday).
 * The day of Jupiter is translated as the day of Donar/Thor, though Thor is generally identified in interpretatio romana as Hercules. (Thursday)
 * The day of Venus is translated as the day of Frija/Frigg. (Friday)