Is it permissible to take money from one's father without his knowledge, despite his prior permission to do so and his forgiveness, and what is the Islamic ruling on that?

It is preferable and more cautious that you seek your father's permission before taking the money, or inform him after taking it to ensure his consent, so that you do not take an excessive amount that he would not permit. Scholars differ regarding the condition of knowing the permissible amount when permission is given. Some scholars are of the view that permission to eat is valid even if the quantity is unknown, whereas a gift is not valid if its quantity is unknown. Others stipulate that the permissible item must be specified unless there is a need.