History
Swedish-born naturalist Carl Linnaeus is credited as the "father of taxonomy," according to the University of California. In "Systema Naturae," first published in 1735, he describes a classification system for all living things. Linnaeus began the trend for reference texts to include fish in the class pisces. In modern classifications, this grouping is no longer used.
Chondrichthyes
Cartilaginous fishes include sharks, rays and skates. These fish have skeletons composed of cartilage and their bodies are covered with triangular placoid scales. The fish's mouth is usually located beneath the head and filled with several rows of sharp, triangular teeth. Class Chondrichthyes have no swim bladder and instead maintain buoyancy solely by swimming. They have paired pectoral and pelvic fins that are stiff, as well as a large caudal fin. Their large, sensitive noses help them hunt more efficiently.
Osteichthyes
The majority of living fishes are bony fishes, accounting for about 20,000 species. These include carp, tuna, bass, perch, catfish, cod, sturgeon and salmon. They are characterized by a skeleton made of bone and paired fins made of spines or rays, or lobed fleshy fins. Osteichthyes have a swim bladder that they use to control their buoyancy. Most lay eggs and have gills covered by a single flap.
Agnatha
Jawless fish such as lamprey and hagfish use sucker-like mouths to attach to prey. The fish have a form of backbone known as a notochord -- a flexible, rodlike structure that was an evolutionary pre-cursor to the backbone found in chondrichthyes and osteichthyes. Agnatha do not have pelvic and pectoral paired fins, instead displaying a rounded snakelike body with a compressed caudal fin. The fish are also devoid of scales and a swim bladder.