It appears to have been inaugurated in the sixteenth century at Safed by the kabbalist Moses Cordovero,[1] who called the fast Yom Kippur Katan; and it was included by Isaac Luria in his Seder ha-Tefillah.
[2] When Rosh Chodesh occurs on Shabbat or Sunday, Yom Kippur Katan is observed on the preceding Thursday.
[3] The custom has roots in scripture (Numbers 28:15) where a sin offering is sacrificed on Rosh Hodesh, indicating judgement and atonement is provided by God on that day.
[5] The selichot are taken partly from the selichos of mincha from Yom Kippur, with the Viddui ha-Gadol (the great confession of sin by Rabbenu Nissim) and Ashamnu, and also a beautiful poem written for the occasion by Leon of Modena and beginning with Yom zeh.
As stated above, if the 29th of the month falls on a Friday or a Sabbath, Yom Kippur Katan is observed on the Thursday prior.