Q. Why do some people fast on the first Monday, Thursday and Monday of Mar-Cheshvan?
A. The same practice is followed on the first Monday, Thursday and Monday of Iyyar. Whilst not of very ancient origin, these fasts follow Pesach and Sukkot to seek forgiveness for any excesses of eating, drinking and levity on the Yom-Tov. The Midrash says that Job was concerned that his sons may have overdone their feasting and he told them to fast as a means of atonement.
Not many people keep these fasts, though at some stage a pious custom developed of a pious fast every Monday and Thursday, which led to the popular saying about people with predictable habits doing things alle Montag und Donnerstag. Monday and Thursday were chosen because these were market days when the Beth Din had court sessions, and there was a belief that the heavenly court sat then too.