Do not be sexually intimate with a married woman (7th of 10 Commandments)
“Do not commit adultery” Shmos 20: 13 and “you shall not lie sexually with your fellow’s wife” Vayikra 18:20
Both he and she are liable for death by strangulation.
If she is the daughter of a Kohen, her death is by burning and his by strangulation.
If she is a betrothed virgin still in her father’s house both are killed by stoning.
All this applies where there were witnesses and a warning.
If it was done intentionally without a warning the punishment is spiritual severance and if done unwittingly a sin offering is required.
This applies in all places at all times