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In Judaism, Shabbat Machar Chodesh, which is when Rosh Chodesh occurs the day after Shabbat (Saturday). On this occassion the Shabbat is termed Shabbat Machar Chodesh, literally meaning, “tomorrow is the [new] month", and a special haftarah is observed involving the new moon.
Here are some ways you can observe this day according to Jewish tradition: