A sage in ancient India. He once consoled the king Dyumasena as per Mahabharata Vanaparva Chapter 298 verse 18.
There’s a story behind the sage’s name. Once a brahmin couldn’t find other brahmins for giving offerings to departed souls (shraadh). He spread the darbha mat and prayed to his forefathers and Vishnu. Then Aapastamba appeared there and the brahmin fed him. After the meal, the brahmin asked him if he was satisfied, and the sage asked for one more morsel. Thus the shraadh was a failure. The brahmin took some water in his hand and proceeded to curse the sage. The sage retaliated by cursing that the water drops would stop in their tracks. Aapa is another word for water and the one who made it stop (sthamba) was thus called Aapasthamba, as per Brahmapurana.
Once he met Agastya and asked who was greater- Brahma, Vishnu or Shiva. Agastya opined that it was Shiva and also taught Aapasthamba the ways to appease Shiva. The sage then started praying to Shiva on the banks of the Gautami river. Shiva was pleased and the place became a holy destination. Shiva decreed that those praying there would obtain divine knowledge. As per Brahmandapurana, the place became known as Aapasthambatheertha.
Aapasthamba had a very chaste wife named Akshasutra. Their son was Garki. Aapasthamba has contributed a Grihyasutrasangraha containing one smriti and 2 mantras. Aapasthamba had noted that there wouldn’t be any rishis in later ages because people wouldn’t be able to control lust.