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A genus is a rank in the biological classification (or taxonomy). It stands above species, and below families. A genus can include more than one species. When biologists talk about a genus, they mean one or more species of animals or plants that are closely related to each other.
When printing the scientific name of an organism, the name is always in italic. A name of species has two parts, with the genus first. For example, in "Felis silvestris", Felis is the genus. The genus name always begins with a capital letter. In "Felis silvestris catus", the third word is the subspecies, which is not often used.
As a common word
In writing, genus names in Latin may be 'anglicised' to form a common name. For example, the genus Pseudomonas is "pseudomonad" (plural: "pseudomonads"). In practice, most really common animals and plants already have a common name. So instead of saying 'felids', or 'felines', one says 'cats'. The word 'cat' is used both for the family pet, and also as a general term for all the cat family (Felidae).