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A calendar is a system for arranging time units for calculating time over long periods. By convention, the day is the smallest unit of time; the measurement of fractions of a day is classified as time measurement. The generality of this definition is due to the diverse methods used to compile calendars. Although some calendars repeat astronomical cycles according to fixed rules, others are based on abstract, constantly repeating cycles of no astronomical significance. Some calendars are regulated by astronomical observations, some contain each unit accurately and redundantly, and some contain ambiguities and discontinuities. Some calendars are codified in written laws; others are transmitted through oral tradition. The common theme of making calendars is the desire to organize time units to meet the needs and businesses of society. In addition to practical purposes, the organizational process offers a sense, how illusory, also the understanding of and time itself. Calendars thus serve as a link between humanity and the cosmos. It is no wonder that calendars held a sacred status and served as a source of social order and cultural identity. Calendars provided the basis for planning agricultural, hunting and migration cycles, for divination and prediction, and for maintaining cycles of religious and civil events. Regardless of their scientific refinement, calendars should ultimately be judged as social contracts, not as scientific treatises. According to a recent estimate (Fraser, 1987), about forty calendars are used in the world today. This chapter is limited to the half dozen major calendars currently in use. Furthermore, the emphasis in the chapter is on function and calculation rather than on culture. The basic basis of the calendars is given, along with brief historical summaries. Although algorithms are given to correlate these systems, it appears carefully that even the standard calendars are subject to local variation. With the exception of the Julian calendar, this chapter does not deal with extinct systems. The inclusion of the Julian calendar is justified by its everyday use in historical studies. Despite a large literature on calendars, it is difficult to find truly authoritative references, especially in English. Aveni (1989) examines a wide range of calendar systems and emphasizes their cultural contexts rather than their operational details. Paris (1982) contains useful but not infallible tables for converting the date. Fotheringham (1935) and the Encyclopedia of Religion and Ethics (1910), in its section on "Calendars", provide basic information on historical calendars. The sections on "Calendars" and "Chronology" in all editions of the Encyclopedia Britannica provide useful historical recordings. Ginzel (1906) remains an authoritative, if dated, standard of calendar science. References to individual calendars are given in the relevant sections.