Tishri opens with the High Holidays (Rosh Hashana and Yom Kippur), which incorporate the Aseret Yamei Tshuva or 10 Days of Penitence. This is considered the season when God is most receptive to our entreaties for forgiveness. The process of atonement requires regret, verbal confession, making all necessary reparations and a sincere intent not to re-offend.
According to tradition, God assesses each individual on Rosh Hashana and passes sentence on Yom Kippur. Apples are dipped in honey and sweet challot are used (till the end of Succot) as we look forward to a sweet new year. The Shofar is sounded for 100 blasts on each day of Rosh Hashana (excepting Shabbat and Erev Rosh Hashana), calling us to repent. It evokes the faith of Abraham, who was prepared to devote his life and even offer up his son at G‑d’s behest.
The Fast of Gedalya on 3 Tishri recalls the assassination of the biblical governor of Jerusalem & Judea who was killed by the Nebuchadnezzar & the Babylonians in the 6th Century BCE.