Craniata: Jawless snake-like fish. Members are hagfishes and lampreys.
-Gnathostomata: Jawed vertebrates. They are the fishes and tetrapods.
--Chondtrichthyes: Cartilaginous fish. Members are sharks and rays.
--Actinopterygii: Ray-finned fishes. They are the dominant fish of the oceans. Goldfish, tuna, carp, piranha, you name it.
--Osteichthyes: Lobe-finned fishes. They include the coeclanth and lungfish. Some ancestral to tetrapods.
---Tetrapoda: The land fish. Dominate the land.
----Amphibia: Semi-aquatic (amphibious) insectivores. They are basal tetrapods and have skin which can't hold water well.
-----Amniota: Tetrapods with a water-tight shell.
------Sauropsida: Scaly or feathery amniotes.
-------Reptilia: The scaly amniotes, they represent roughly half of amniotes. They are the Crocodilians, Tuatara, Squamates, and Testudines.
-------Aves: The birds. Another subclass of Sauropsida.
------Mammalia: Mammals, the furred, live-bearing animals with parental care.
You should be familiar with them (as you are a mammal).
Cephalochordata: Brain-less fish-like burrowing filter feeding organisms.
Urochordata: Bags of jelly. Commonly called Tunicates or Sea Squirts.