The main purpose of reading the Torah in public is, of course, to teach, that the people shall know the Torah. (See INTRODUCTION TO THE SIDRA OF THE WEEK.) For this reason, too, the public Torah reading was arranged also to include topical teachings. That is, before a Yom Tov and on the Yom Tov, the Dinnim of the Yom Tov would be read. This way, the people were prepared for the coming Yom Tov and indeed were informed of its date.
There are not many Dinnim about Rosh Chodesh, the day that marks the new month (or sometimes, in the case of two days of Rosh Chodesh, the last day of the previous month and the first day of the new month). The institution of Rosh Chodesh is primarily the concern of the Beis Din HaGa’dol in Yerushalaim that they should proclaim Rosh Chodesh and thus fix the Yommim Tovim (see SIDRA OF THE WEEK: בא) and a special Korban Mussaf is brought in the Beis HaMikdash on Rosh Chodesh, too. But as far as the individual is concerned, the public Torah reading of Rosh Chodesh serves as an announcement of Rosh Chodesh, that is, that this day marks the beginning of the new month.
The Jewish calendar is a lunar-solar calendar, meaning, it is governed and regulated by the moon but it is at the same time also a solar calendar. That is, HaShem has ordained in His Torah that the Yommim Tovim of the yearly cycle shall be dated according to the moon, namely, such-and-such a day in the lunar month (really, of course, there is no such thing as a solar “month”!) but with built-in adjustments to ensure that each of the Yommim Tovim falls in its particular season of the year (and the seasons are, of course, brought about by the sun). That is what is meant when we say that the Jewish calendar is a lunar-solar calendar. Knowing when is Rosh Chodesh is very important to the Jewish People because of the date of the Yommim Tovim and, as said, this is the reason that there is a public Torah Reading on Rosh Chodesh.
The Rosh Chodesh Torah Reading is taken from the Sidra Pinchos in Sefer BeMidbor. When Rosh Chodesh is on a weekday there are four Aliyos (Rosh Chodesh is, so to speak, a step “higher” than the ordinary weekday whose Torah readings have only three Aliyos) and therefore the Torah Reading of Rosh Chodesh starts at the beginning of Chapter 28 and includes also the section which teaches of the daily Korban Tommid, followed by the Shabbos Korban Mussaf, ending with the Korban Mussaf of Rosh Chodesh.
When Rosh Chodesh falls to be on a Shabbos, the Rosh Chodesh Torah Reading is appended to the Sidra of the Week and is read as the Maftir. In that case, the reading starts from Possuk 9 and ends with Possuk 15.
Usually on Shabbos Rosh Chodesh, two Sifray Torah are taken out and the Maftir is read from the second Sefer Torah, after the Sidra of the Week. If there is only the one Sefer Torah, then after the Sidra of the Week has been read, the Sefer Torah is rolled to Sidra Pinchos for the Maftir. There is a special Haftorah for Shabbos Rosh Chodesh which usually (but not always) takes the place of the week’s Haftorah.
