Halakha, from a root meaning to go or to walk, is the body of Jewish law and, equally, the process by which that law is determined. It covers worship, diet, the Sabbath and festivals, purity, marriage and divorce, business, torts, and the conduct of courts, without the division between religious and civil law that later Western systems assume. To ask what halakha says about something is to ask what a Jew is obligated to do.
Its literary sources form a chain. The written Torah; the oral Torah as compiled in the Mishnah about 200 CE and expounded in the two Talmuds, of which the Babylonian, closed around 500-600 CE, became authoritative; the responsa of the Babylonian geonim; then the great codes, Maimonides' Mishneh Torah (c. 1180), Jacob ben Asher's Arba'ah Turim, and Joseph Karo's Shulhan Arukh (1565), which achieved general authority only once Moses Isserles supplied glosses recording Ashkenazi practice. Alongside the codes runs a responsa literature, case law in the form of answered questions, that has never stopped being written.
Traditional accounts hold that the oral Torah was given at Sinai together with the written and transmitted in an unbroken chain, a claim stated at the opening of tractate Avot. Historical-critical scholarship describes instead a developing interpretive tradition whose institutions and methods can be traced through the Second Temple period, the rabbinic academies and the medieval centres. The two accounts are not describing different laws; they differ over the status and the origin of the process, and that difference is one of the things the modern movements divide on.
The familiar count of 613 commandments, 248 positive and 365 negative, is a rabbinic enumeration attributed to R. Simlai in the Talmud, and the lists that later authorities drew up to fill it out do not agree with one another; Maimonides' Sefer ha-Mitzvot is the most influential, and Nahmanides' criticism of it the most influential reply.