Mithra was the most important Zoroastrian god on the side of Truth. He was the god of contracts and keeping your promises, like the German god Tyr. He's related to the Hindu god Mitra, mentioned in the Rig Veda, who was also a god of honesty and contracts. Because the farming people of the Persian Empire were always fighting with the nomads around them, Mithra also began to represent civilization, order, and living in one place as opposed to crime, confusion, and always moving around (this is from the point of view of the settled people! the nomads weren't really criminals).
Mithra approving as Ardashir becomes the Sassanid king (200s AD)
When Roman soldiers fought in the East (that is, in West Asia), they saw their enemies praying to Mithra. They thought he must be a very strong god, and began trying to take him over for themselves. They didn't know much about Zoroastrianism, though, so they worshipped Mithras (they called him Mithras) very differently from the way the Persians worshipped him.
An underground mithraeum in Ostia
By the 200s AD there were shrines to Mithras all over the Mediterranean coasts and all through Europe, everywhere that soldiers were stationed. There was even a complicated set of rituals you could go through that would make Mithras like you more and think you were special, which involved things like pulling out your hairs one by one.
When Christianity became the official religion of the Roman Empire in the 300s AD, people worshipped Mithras less and less, and by 400 AD you hardly hear of Mithra anymore in Europe or around the Mediterranean. In West Asia, where Zoroastrianism continued to be the official state religion until nearly 700 AD, Mithra continued to be worshipped. But when Islam came to West Asia about 700, and Zoroastrianism declined, so did the worship of Mithra.
Zoroastrianism, by Paula Hartz (updated 2004). Easy reading.
The Usborne Book of World Religions, by Susan Meredith (1996). Easy reading.
An Introduction to Ancient Iranian Religion: Readings from the Avesta and Achaemenid Inscriptions, by William Malandra (1983). A nice clear explanation of ancient Zoroastrianism.
The Roman Cult of Mithras: The God and His Mysteries, by Manfred Clauss (2001). This is mainly about Roman Mithraism, not the original god in Persia.
Ancient Mystery Cults, by Walter Burkert (reprinted 1989). Burkert is a leading expert in ancient religion, and this is a great book! One of the chapters of this book is on Mithraism. Too hard for kids.
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