This chapter discusses ancient number systems, beginning with the Babylonian system. Almost every history of early Western mathematics begins with the Babylonian conception of number, a so-called sexagesimal (base 60) system for writing large numbers, formulations of multiplication tables, and ideas for astronomy. The current number system needs symbols for just ten numbers in order to represent any number we wish, compared to that of the Babylonians which needed just two symbols. The chapter also considers the early Egyptian number writing, which was an additive system, as well as the Greek alphabet and sequential number system, Roman numerals, Aztec numerals, and the Mayan system.