Is one allowed to fish for entertainment purposes even he plans to throw back the fish if the fish is caught or is this considered improper?
As part of fishing for food, a fly-fisher often releases fish back to the river. This is perfectly permitted, because the general purpose is for food. If, however, the entire purpose in only for the sake of entertainment, authorities frown at the pastime (see Mishnah Halachos 12:432), due to considerations of cruelty to animals. I recommend fishing for the sake of actually eating the fish, through which the halachic considerations are solved, and one can also enjoy the experience of fishing.