How many cat species are there?

Depending on whose version of taxonomy that you rely on there are between 36-41 species of cat. The variation is because some scientists treat subspecies as species and vice versa. If you treat a species as a subspecies it reduces the number of species. If you treat a subspecies as a species then the number rises. This latter scenario is more common and why Wikipedia list 41 or 40 species of cat.

Personally I rely on the famous book: Wild Cats Of The World by Mel and Fiona Sunquist who list 36 species. On my website (PoC) I list 37. The reason given is stated on this page which is the first of two pages on all the wild cat species.

Note: "species" is not "breed". Species is a scientific term within the science of taxonomy while "breed" is a cat breeder's term. All breeds are one species felis silvestris catus.

You can see a full page written in straightforward English on the wild cat species by clicking this link. Hope this helps.