What term is used for the rearing and breeding of birds?

Aviculture is the practice of keeping and breeding birds, especially wild birds in captivity. Aviculture is generally focused on not only the raising and breeding of birds, but also on preserving avian habitats, and public awareness campaigns. Aviculture has a broad definition and can include anyone who keeps birds as pets, and breeds birds as a hobby or a business, including even raising chickens for selling their eggs or meat.

Source: Association of Avian Veterinarians