CHAZAL חז״ל - an acronym for these word "Chachameinu Zichronam Livracha" (our saves of blessed memory). "Chacham" means wise - so "Chachameinu" could literally be translated as "our wise ones". "ZACHAR" is the verb to remember, thus the root of "Zichronam" - maybe they be remembered. LIVRACHA - is broken down L'-Bracha - for a blessing. The "B" or "BET" of Bracha changes to a "V" or "VET" in this case. When you see something looks like a double-quote in a Hebrew word, it is often a hint that the word is an acrnoym.
RISHONIM - the leading Rabbis and Poskim who lived approximately during the 11th to 15th centuries, in the era before the writing of the Shulkhan Arukh and following the Geonim. Source: http://en.wikipedia.org/wiki/Rishonim
Acharonim (Hebrew: אחרונים; lit. "last ones") is a term used in Jewish law and history, to signify the leading rabbis and poskim (Jewish legal decisors) living from roughly the 16th century to the present. The Acharonim follow the Rishonim, the "first ones" - the rabbinic scholars between the 11th and the 16th century following the Geonim and preceding the Shulkhan Arukh. The publication of the Shulkhan Arukh thus marks the transition from the era of Rishonim to that of Acharonim. Source: http://en.wikipedia.org/wiki/Acharonim
Tannaim- (Hebrew: תנאים, singular תנא, Tanna) were the Rabbinic sages whose views are recorded in the Mishnah, from approximately 70-200 CE. The period of the Tannaim, also referred to as the Mishnaic period, lasted about 130 years. It came after the period of the Zugot ("pairs"), and was immediately followed by the period of the Amoraim. Source: http://en.wikipedia.org/wiki/Tanaim
The root tanna (תנא) is the Talmudic Aramaic equivalent for the Hebrew root shanah (שנה), which also is the root-word of Mishnah. The verb shanah (שנה) literally means "to repeat [what one was taught]" and is used to mean "to learn".
The Mishnaic period is commonly divided up into five periods according to generations. There are approximately 120 known Tannaim.
Amora - (Aramaic: אמורא; plural אמוראים, Amora'im; "those who say" or "those who tell over"), were renowned Jewish scholars who "said" or "told over" the teachings of the Oral law, from about 200 to 500 CE in Babylonia and the Land of Israel. Their legal discussions and debates were eventually codified in the Gemara. The Amoraim followed the Tannaim in the sequence of ancient Jewish scholars. The Tannaim were direct transmitters of uncodified oral tradition; the Amoraim expounded upon and clarified the oral law after its initial codification.
Savora - (Aramaic: סבורא, plural Savora'im, Sabora'im, סבוראים) is a term used in Jewish law and history to signify the leading rabbis living from the end of period of the Amoraim (around 500 CE) to the beginning of the Geonim (around 700 CE). As a group they are also referred to as the Rabbeinu Sevorai or Rabanan Saborai, and may have played a large role in giving the Talmud its current structure. Modern scholars also use the term Stammaim (Hebrew = closed, vague or an unattributed source) for the authors of unattributed statements in the Gemara. Source: http://en.wikipedia.org/wiki/Savoraim
Geonim (Hebrew: גאונים; also transliterated Gaonim) were the presidents of the two great rabbinical colleges of Sura and Pumbedita, in Babylonia, and were the generally accepted spiritual leaders of the Jewish community world wide in the early medieval era, in contrast to the Resh Galuta (Exilarch) who wielded secular authority over the Jews in Islamic lands.
Geonim - is the plural of גאון (Gaon'), which means "pride" or "splendour" in Biblical Hebrew and since the 1800s "genius" as in modern Hebrew. As a title of a Babylonian college president it meant something like "His Excellency."
The Geonim played a prominent and decisive role in the transmission and teaching of Torah and Jewish law. They taught Talmud and decided on issues on which no ruling had been rendered during the period of the Talmud.
The period of the Geonim began in 589 (Hebrew date: 4349), after the period of the Sevora'im, and ended in 1038 (Hebrew date: 4798). The first gaon of Sura, according to Sherira Gaon, was Mar Rab Mar, who assumed office in 609. The last gaon of Sura was Samuel ben Ḥofni, who died in 1034; the last gaon of Pumbedita was Hezekiah Gaon, who was tortured to death in 1040; hence the activity of the Geonim covers a period of nearly 450 years.
There were two major Geonic academies, one in Sura and the other in Pumbedita. The Sura academy was originally dominant, but its authority waned towards the end of the Geonic period and the Pumbedita Gaonate gained ascendancy (Louis Ginzberg in Geonica).
Zugot - (Hebrew: תְּקוּפָת) הַזוּגוֹת)) ((təqūphāth) hazZūgh?th) refers to the period during the time of the Second Temple (515 BCE - 70 CE), in which the spiritual leadership of the Jewish people was in the hands of five successive generations of zugot ("pairs") of religious teachers. Source: http://en.wikipedia.org/wiki/Zugot In modern Hebrew, zugot (or zugim?) can mean "twins". The English word "Zygot" (in the field of biology) comes from this Hebrew word. (is a term in Developmental biology used to describe the first stage of a new unique organism when it consists of just a single cell)