The Mishnah was compiled around 200 CE under Judah ha-Nasi, gathering into writing the oral legal tradition of the tannaim, the rabbis of the preceding two centuries. It is arranged in six orders. Zeraim covers agriculture and, in its opening tractate, blessings and prayer; Moed the Sabbath and festivals; Nashim marriage, divorce and vows; Nezikin civil and criminal law, courts and, in tractate Avot, ethics; Kodashim sacrifices and the Temple; and Tohorot ritual purity. Much of Kodashim and Tohorot concerns a Temple destroyed in 70 CE and describes a system nobody could still practise, the Mishnah records the law as a whole, not only the part currently operable.
Its style is extremely compressed: a ruling, often a named dissent, rarely a reason. The Gemara is the analysis that grew around it in the academies over the following three centuries, written mostly in Aramaic by the amoraim. It asks where a rule comes from, whether it contradicts another, what case it was really addressing, and whether the dissenting view can be reconciled.
Together Mishnah and Gemara are what Jews call the Oral Torah written down: tradition holds that law transmitted orally from Sinai alongside the written text was committed to writing only when persecution and dispersion threatened its survival. Its unit of argument is the sugya, a self-contained discussion that states a difficulty, proposes answers, tests them against other sources and often ends unresolved. A frequent closing word is teiku, indicating that the question stands. The Talmud teaches how to argue about law at least as much as it delivers conclusions.