The noun αιων (aion) means life-span, age or epoch. It is the source of our English words age and eon, and ultimately stems from the Proto-Indo-European root "heyu-" meaning the same.

Our noun appears to describe any length of clearly defined span of time, whether one person's life or some era of certain renown. As general point of referral, this word may also apply to the vast span of history: the ages, the times of old. It's used 126 times in the New Testament; see full concordance

Note that the Greeks also applied this word to the spinal marrow, which appears to suggest that they saw society as much based on social evolution as a human being on his spinal cord. To the Greeks, time wasn't merely the stage upon which all things unfolded. Instead they realized that time is an inherent and fundamental quality of the universe that doesn't exist separate from it (something moderns didn't know until Einstein). They personified abounded but cyclical time, or "the ages" as the deity Aion and associated him with a coiling snake that often ate its own tail or else curled along a spoke or spine.

In Roman times, Aion began to personify the eternal Roman rule, which made him/it an obvious target of the New Testament writers (Matthew 6:13, Luke 1:33, Romans 1:25). The Roman Aion even begat a female counterpart named Aeternitas (from which we have our English word eternity) who adopted the patronage of the deified Roman Emperor. This in turn made her too an obvious topic of commentary for the earliest church fathers.

From this noun comes:

The adverb αει (aei) means always, ever, continually, and stems from the same PIE root as the above. It's used 8 times in the New Testament, see full concordance, and from it comes: