Elon Musk wants to terraform and colonize Mars. With advancing technology, would it be possible for humans to colonize the moon?

Possible?

Maybe.

Probable?

I don't think so.

Without an atmosphere, terraformation would have to end with anaerobic “organisms” capable of withstanding heat and/or cold extremes that humans cannot survive in without EXTENSIVE body coverings. Any moon colony, even if it occupied space beneath the moon’s surface, would totally depend on technology for oxygen and moderation of temperature extremes. If temperature control or oxygen generation/distribution was compromised, the colony would last minutes at the most.

That being said, 100-years ago, the idea of humans walking on the moon's surface was considered impossible.