It is in the Mishnah, the oral law that preceded the Talmud compiled in Israel by Yehuda Hanasi, that we are first introduced to the main theme of the holiday, that of judgment: “On Rosh Hashanah all human beings pass before him [God] as sheep before a shepherd” (Tractate Rosh Hashanah 2)
Source: Haaretz, “The history of Rosh Hashanah, which wasn’t always the ‘new year,’” September 2, 2014.
“Yom Kippur atones for transgressions between a person and God…” (Misha Yoma 8:9)