Classification
The traditional classification of vertebrates is a mess, with a wide variety of paraphyletic groups that have either been abandoned or extended (here marked B). Unfortunately, no particularly standard system has settled in to replace it; the problem is there have been too many adaptive radiations. For now, here is a minimal tree of living forms including most traditionally class-sized groups:
Urochordata
Cephalochordata
Craniata
Myxini (hagfish)
Vertebrata
Petromyzontiformes (lampreys)
Gnathostoma
Chondrichthyes (cartiligenous fish)
Osteichthyes B
Actinopterygii (ray-finned fish)
Sarcopterygii B
Coelocanthamorpha
Dipnoi (lungfish)
Tetrapoda
Lissamphibia (frogs, toads, salamanders)
Amniota
MammaLia
Chelonia (turtles)
Squamata (lizards, snakes)
Sphenodontida (tuataras)
Crocodylomorpha (crocodiles, alligators)
Aves (birds)
Information on characteristics of each group and a more detailed classification thereof should probably go under its headline - eg details of skeletal system and listing of jawless fishes under Vertebrata.