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Bircat HaChammah—a ritual performed once every 28 years, to mark the belief that the sun has returned to its exact position at creation. Last performed on April 8, 2009, it is one of two Jewish rituals that depend on the solar calendar; the other is the date for recitiation of Tein Tal U'Matar in the Diaspora. Whenever a century year is not divisible by 400 (e.g. 2100), the date, which matches the Julian calendar, not the Gregorian, advances one day due to the "missing" February 29 (e.g. after 2100, it will be recited on April 9 in the applicable years). Here is a table of days when Bircat HaChammah is recited.
Chanukah—the winter holiday commemorating the rededication of the Temple during the Maccabean revolt. It is observed for 8 days starting on 25 Kislev; the main observance is the nightly lighting of the Chanukiah, a 9-branched menorah (candelabrum). It is traditional to eat foods fried in oil, especially latkes (potato pancakes) and jelly doughnuts (sufganiyot). Full hallel is recited all 8 days, even on Rosh Hodesh Tevet, and a special prayer (Al ha-nisim) is added to the Amidah at all services. More information.
Hallel—Psalms of praise—113, 114, 115, 116, 117, and 118. The entire group of 6, Full Hallel, is recited during Shacharit on Sukkot (all days), Shavuot, Pesach (first day only in Israel, first 2 days outside for Orthodox and Conservative), and Chanukah; some also recite it on Yom HaAtzmaut and Yom Yerushalayim, and some during Maariv on the first night(s) of Pesach. An abbreviated version, Half Hallel, omitting the first 11 verses of 115 and 116, is recited on the last 6 days of Pesach, and Rosh Hodesh. A bifurcated version is also recited at the Passover seder, 113 and 114 before the meal, and 115 through 118 after.
Hol Hamoed—the intermediate days of festivals. In Israel, this is the second through sixth day of Pesach and the second through seventh day of Sukkot. For Orthodox and Conservative elsewhere, it is the third through sixth day of Pesach and the the third through seventh day of Sukkot. Half hallel is recited on Pesach; full hallel on Sukkot. On Shabbat, there is a special Torah portion and Haftarah; on weekdays, Ya'aleh v'yavo is read as part of the Amidah at all services (and as part of Bircat Hamazon), there are 4 aliyot for a special Torah reading, and musaf is recited. More information.
Kabbalat Shabbat—welcoming the Sabbath. A selection of prayers before the start of maariv on Friday night. When either Friday or Saturday coincides with Yom Tov (including Hol Hamoed), an abbreviated version (Psalms 92 and 93 only) is recited. More information.
Maariv—The evening prayer service, recited every day. Also known as Arvit. More information.
Mashiv haRuach/Morid haTal—From musaf on Shemini Atzeret through Shacharit on the first day of Pesach, the phrase "mashiv haruach u'morid hagashem", "who causes the wind to blow and the rain to fall", is added to the Amidah. During the rest of the year, Ashkenazim typically omit the phrase, while Sephardim typically substitute "morid hatal", "who causes dew to fall".
Mincha—The afternoon prayer service, recited every day. More information.
Musaf—An additional recitation of Amidah and a special Kedushah, recited immediately after the Shacharit Torah service on the days of the extra sacrifices enumerated in Numbers chapters 28 and 29. These are Shabbat, Rosh Hodesh, Yom Tov, and Hol Hamoed.
Passover/Pesach—the spring holiday which commemorates the liberation from slavery. It starts on Nisan 15; Orthodox and Conservative outside of Israel celebrate for 8 days, with the first two and last two Yom Tov and the middle four Hol Hamoed; in Israel, and for Reform outside, it is celebrated for 7 days, with the first and last being Yom Tov and the middle 5 Hol Hamoed. The most notable feature of Pesach is to refrain from eating hametz (any leavened food) – unleavened bread, matzah, is a staple for the holiday. A ceremonial home service and meal, the seder, is held on the first night(s). The counting of the omer begins with the second night. Tal, the prayer for dew, is recited as part of the musaf service on the first day; we stop saying Mashiv Haruach, and starting saying Tein Tal U'Matar. Yizkor is recited on the last day. More information.
Purim—the holiday marking the saving of Persian Jewry by Queen Esther. It is celebrated with a boisterous reading of the Megillah (Book of Esther), with children dressed in costumes and using noisemakers known as groggers. It is also marked by sending gifts of food (especially cookies known as hamantaschen) to friends. It is mainly celebrated on Adar 14 (Adar-II in leap year), but, in ancient walled cities (Jerusalem), it is instead celebrated on Adar 15, which is known as Shushan Purim. Adar 13 (or 11 if 13 falls on Shabbat) is the half-day Fast of Esther. More information.
Rosh HaShanah—the beginning of the Hebrew year, celebrated for 2 days on Tishri 1/2 even in Israel (Reform outside marks 1 day only), the days are marked with very elaborate and long services marking the beginning of a period of deep introspection, the 10 days of repentance, which culminate in Yom Kippur. Among the many sections added to the service are un'tane tokef, hineni, malchuyot, zichronot, and shofarot. The shofar is sounded except on Shabbat. Tashlich happens on the first afternoon, or on the second if the first is Shabbat. More information.
Rosh Hodesh—the beginning of the Hebrew month. It is, naturally, observed on the first day of each month (except Tishri, whose first day is Rosh Hashanah); in addition, the last day of months with 30 days is also observed as Rosh Hodesh for the following month. Half hallel is recited (full hallel for Tevet because of Chanukah). On Shabbat, there is a special maftir and haftarah; on weekdays, there are 4 aliyot for a special Torah reading. Ya'aleh v'yavo is read as part of the Amidah at all services (and as part of Bircat Hamazon), and musaf is recited. As part of musaf, Hadesh Alenu asks for 12 different blessings, one for each month of the year; in leap years with 13 months, a 13th blessing (ul'chaparat pasha) is added. Psalm 104 (Barchi Nafshi) is recited after the psalm of the day.
Shabbat—Sabbath, the day of rest. The holiest day of the Jewish week, observed starting with candle lighting before sunset on Friday and concluding with havdalah after sunset Saturday. (FYI, here is a surprising view on Shabbat in the Far East and West). There is far more to be said about it than can reasonably be placed here; here's a start.
Shacharit—The morning prayer service, recited every day. More information.
Shavuot—the feast of weeks, so called because it comes 7 weeks after Pesach. It is celebrated as the date on which the Torah was given. In Israel, and for Reform, it is celbrated for 1 day; for Orthodox and Conservative outside Israel for 2 days. More information.
Shemini Atzeret/Simchat Torah—a separate Yom Tov following immediately after Sukkot. In Israel, and for Reform, the days are combined on Tishri 22; Orthodox and Conservative mark Shemini Atzeret on Tishri 22 and Simchat Torah on Tishri 23. On Shemini Atzeret, Geshem, the prayer for dew, is recited as part of the musaf service; we resume saying Mashiv Haruach. Yizkor is also recited. On Simchat Torah, we make many processions, Hakafot, with the Torah at both Maariv and Shacharit; we uniquely read from the Torah at Maariv; at Shacharit, we conclude the annual Torah reading with the final chapters of Deuteronomy, and start all over at the beginning of Genesis. More information on Shemini Atzeret. More information on Simchat Torah.
Sukkot—the autumn Feast of Tabernacles. It starts on Tishri 15 and lasts 7 days. The first day (first 2 for Orthodox and Conservative outside Israel) is Yom Tov; the rest are Hol Hamoed, with special observances on the seventh day, Hoshana Rabbah.. People eat all their meals, and even sleep, in a temporary dwelling, the sukkah. On all days except Shabbat, a blessing is made over the lulav and etrog. After Musaf, processions known as Hoshanot take place in the synagogue. More information.
Tisha B'Av—the most calamitous day of the Jewish year, on which both the First and Second Temples were destroyed, and many other disasters occurred. It is observed on the 9th of Av, or the 10th if the 9th is Shabbat. It is marked by a full sunset-to-sunset fast, the recitation of the Book of Lamentations, and other mourning rituals. There are many changes to the daily service. More information.
Tein Tal U'Matar/Tein B'racha—In the weekday Amidah, either "tein tal u'matar liv'racha" ("give dew and rain for blessing") or "tein b'racha" ("give blessing") is recited. "Tal u'matar" always starts with the first day of Hol HaMoed Pesach; in Israel, it is recited through Heshvan 6. In the Diaspora, the end date is one of two Jewish rituals depending on the solar calendar (the other is Bircat haChammah). and has a complicating dependence on the Julian calendar. For the period from 1900-2100, it is recited through mincha on Dec. 4 (or Dec. 5 in years preceding a civil leap year, e.g. through Dec. 5, 2011; equivalently, it is through Dec. 5 when the Hebrew year is divisible by 4, e.g. Dec. 5 2011 will be in year 5772). Whenever a century year is not divisible by 400 (e.g. 2100), there is no Feb. 29 in the year, and the end date consequently advances one day (e.g. after 2100, it will be recited through mincha on Dec. 5 or 6). Here is a table of days when Tal Umatar is first recited at Maariv each year.
Yom Kippur—the Day of Atonement, the holiest day of the Hebrew year, observed on Tishri 10. The culmination of the 10 days of repentance begun on Rosh Hashanah, this is the day on which one's fate is sealed for the new year. A full sunset-to-sunset fast takes place, and services last for much of the day. Kol Nidre is added before Maariv. Among the many sections added to the Shacharit/Musaf service are un'tane tokef, hineni, martyrology, avodah, yizkor, selichot, and vidui. After Mincha, at which the Torah and a haftarah, the Book of Jonah, is read, a fourth daily service, Neilah, is recited. The shofar is sounded to end the day. More information.
Yom Tov—A holiday ordained in the Torah. These are Rosh Hashanah, Yom Kippur, Sukkot first day, Shemini Atzeret, Pesach first and seventh days, and Shavuot. Outside Israel, Orthodox and Conservative practice is to include the second day of Sukkot, Simchat Torah, the second and eighth days of Pesach, and the second day of Shavuot to this list. A second day of Rosh Hashanah is observed within Israel, and by Orthodox and Conservative worldwide. Yom Tov is always ushered in with candle lighting before sunset.