Does a mother's crying upon her son's departure, despite her permission for him to travel, fall under the meaning of the Hadith: "Go back to them and make them laugh as you made them cry"? And how should he act if she cries upon his departure for seeking knowledge, even though she has given permission?

If your mother gives you permission to travel in pursuit of knowledge, then there is no blame upon you. Her crying is natural due to sadness over your departure. The aforementioned hadith pertains to voluntary jihad, which requires the permission of the parents, whereas obligatory jihad does not require their permission. We advise you to stay in touch with your mother, check on her well-being, and not prolong your absence.