Is it permissible to travel seeking religious knowledge without the parents' permission, and what is the ruling if they do not allow it, and is it true that Imam Ahmad saw no harm in that?

If seeking knowledge is an individual obligation (fard ayn), it does not require the parents' permission. However, if it is a communal obligation (fard kifayah) or a supererogatory act (nafilah), then their permission is necessary. This is because seeking knowledge is a type of jihad, and one is not permitted to volunteer for jihad without the parents' permission. Imam Ahmad was asked about this and said, regarding a student of knowledge who does not know how to pray or perform ablution (literally, "how to pray or divorce"): "Seeking knowledge is dearer to me." But for one who knows these things, "staying in their service (i.e., parents) is dearer to me." If seeking knowledge is indispensable, then there is no harm.