Cultural number systems are the counting numbers one, two, three, their representations in various physical and spoken forms, and the arithmetic and mathematics performed with them. Different societies develop different number systems, and individual number systems change over time. Historically, this variability between and within cultures has been difficult to explain, especially when the human brain is considered to be the reason why number systems differ, the approach of the cognitive sciences. This book takes instead a novel archaeological approach: cultural number systems are studied here through their material component: the fingers, tallies, tokens, and written notations used to represent and manipulate numbers. By focusing on the material component, the archaeological approach is able to explain cross-cultural numerical variability as a matter of whether devices are used, which ones are used, and how they are used. The use of ethnographic data is also detailed. Early ethnographic sources provide important insight into what particular number systems were like before they were greatly influenced by Western contact, but such records must be used with caution.