Judaism (Yahadut in Hebrew) in its simplest definition is the embodiment of the religion, culture, and legal structure of the Children of Israel.
There are two main factions in Judaism: Rabbinic and Karaite.
Rabbinic Judaism – Yahadut Rabanit (יהדות רבנית) – grew out of Pharisaic Judaism and has been considered the mainstream form of Judaism since the codification of the Babylonian Talmud. With the redaction of the “Oral Torah” and the Babylonian Talmud becoming the authoritative interpretation of the Tanakh, Rabbinic Judaism became the dominant form of Judaism in the Diaspora. Rabbinic Judaism encouraged the practice of Judaism when the sacrifices and other practices in the Land of Israel were no longer possible.
When the Romans were attempting to breach the walls of Jerusalem, Yohanan ben Zaccai abandoned Jerusalem even though the Temple still stood. He foresaw the fall of Jerusalem and had himself smuggled out of the city in a coffin in order to speak to the Romans (Gittin 56a-56b).1,2 There can be no historical proof of this tale but the narrative in the Talmud shows the shift in the religious and political life of the Jews following the destruction of the Second Temple. The narrative about the founding of Yavneh in fact represents the birth of Rabbinic Judaism. A way that focused on Torah and halakhah (Jewish law) rather than Temple worship.1
Rabbinic Judaism, as opposed to Karaite Judaism, is based upon the belief that the Prophet Moses received from God not only the Written Torah but also an Oral Torah. This Oral Torah was given as additional oral explanations of the revelation at Mount Sinai. According to Rabbinic Judaism, tradition has the binding force of law. The revelation to the Prophet Moses consisted of both the Written Torah and the Oral Torah along with the implied exposition by the sages of Israel (Berachot 5a).3,4
The validity of the Oral Torah was challenged by the Sadducees. Josephus records that the Sadducees held that the only obligatory observances are those in the Written Torah. After the destruction of the Temple by the Romans the Sadducees disappeared and the body of tradition continued to grow. New rites were introduced as replacement for rituals that had been performed in the Temple (Megilah 31b).3,5 Rabbinic Judaism recognizes the Oral Torah as divine authority and follows the Rabbinic procedures used to interpret the Tanakh.
Even though not all sects within Rabbinic Judaism view the Oral Torah as being binding halakhah, each sect does define itself as coming from the tradition of an Oral Torah. Maimonides wrote the Mishneh Torah showing a direct connection between the Written Torah and the explanations in the Oral Torah. In addition, Rabbi Yosef Caro produced the Shulkhan Arukh which has become the “most comprehensive compendium of Jewish law and tradition to this day.”3
Rabbinic Judaism, in its classical writings produced from the first through the seventh century of the Common Era, sets forth a theological system that is orderly and reliable. Responding to the generative dialectics of monotheism, Rabbinic Judaism systematically reveals the justice of the one and only God of all creation. Appealing to the truths of Scripture, the Rabbinic sages constructed a coherent theology, cogent structure, and logical system to reveal the justice of God. These writings identify what Judaism knows as the logos of God—the theology fully manifest in the Torah. (Jacob Neusner – “Rabbinic Judaism: The Theological System”)6 
According to the followers of Yahadut Qara’it – Karaite Judaism, it is the original form of Judaism as shown throughout the Tanakh from the time of the Revelation beginning at Mount Sinai. Karaites are a sect of Judaism that believes only in the authority of the Tanakh. Karaite Judaism truly began with the national revelation at Mount Sinai. Those who followed God’s laws were at first called “Righteous” as seen in Numbers 23:8.7,8 It was really only in the ninth-century CE that the followers of God’s law began being called Yahadut Qara’it (קראית יהדות). At first, everyone who followed Torah were of one mind and one sect – that of the Yahadut Qara’it.
Throughout Jewish history a variety of sects – such as the Sadducees, Boethusians, Ananites, and Pharisees – came into existence. It was in this atmosphere that the followers of Torah became known as the Yahadut Qara’it.7 At the end of the Biblical period – in the first century BCE – two opposing sects came into being in Israel. The Sadducees followed only the Torah as sacred text. Josephus explains that the Sadducees “take away fate, and say there is no such thing, and that the events of human affairs are not at its disposal; but they suppose that all our actions are in our own power, so that we are ourselves the causes of what is good, and receive what is evil from our own folly.”9 The Pharisees taught of an “Oral Torah” that was added to the Written Torah. This sect taught “that some actions, but not all, are the work of fate, and some of them are in our own power, and that they are liable to fate, but are not caused by fate.”9
Two additional sects arose during the Second Temple Period – the Essenes and the Boethusians. The Essenes was a sect of Judaism that added several books to the Torah. They taught “that fate governs all things, and that nothing befalls men but what is according to its determination.”9 The Boethusians were a sect like the Sadducees who only followed the Written Torah and rejected any additions to the mitzvot given to the Prophet Moses.1
In the early Middle-Ages the Pharisees continued to thrive and began calling themselves “Rabbis.” In the seventh-century the Muslims completely swept the Middle-East. They had no real interest in imposing Islam on the Jews and gave them a degree of autonomy under a system of Rosh Galut (גלות ראש). With the establishment of the Rosh Galut, the Rabbinates became a political power throughout the Middle-East. They began to force upon all Jews within the Empire the Rabbinate laws contained within the Babylonian Talmud. There was fierce resistance to the Rabbinates by those who had never heard of the Babylonian Talmud. One resistance leader, Abu Isa al-Isfahani, led an army of Jews against the Muslim government. However all attempts to cast off the Rabbinate rulers failed.7
In the eighth-century, Anan ben-David organized various non-Talmudic Jewish groups and lobbied the Caliphate to establish a second Rosh Galut for those Jews who refused to follow the man-made laws of the Babylonian Talmud. The Muslims granted Anan and his followers the freedom to practice Judaism as their ancestors had practiced it. Anan was not a Karaite but he did reject the Talmud. His followers became known as Ananites and this group continued to exist until the tenth-century.
Another group of Jews who continued to practice Judaism only according to the Tanakh became known as B’nei Miqra (Followers of Scripture). Their name was shorted to Kara’im (Scripturalists) which became transliterated to Karaites.7 Even though Karaites live and worship only according to the Tanakh, the Tanakh is not taken literally. Karaites believe that every text, including the Tanakh, needs some type of interpretation. However, Karaites believe that the interpretation of the Tanakh must be based upon the peshat (plain) meaning of the text as it would have been understood by the Israelites when it was given based upon proof-texts from the Tanakh, the peshat meaning of the text, and the Hebrew grammar of the text.
Karaites do not accept the idea of an “Oral Torah” nor do they follow the teachings as set down in the Mishnah or Talmud. Karaites are known to study the Mishnah and Talmud as well as other Rabbinic writings since they can hold clues to help everyone understand the Tanakh and Jewish history and philosophy. These writings are simply used as commentary and nothing more. In addition, Karaites completely reject the Zohar, Tanya, and any other mystical teachings since they are considered counter to the Torah.
The Karaites follow the mandates of the yomim tovim (holidays) as prescribed in the Tanakh which means that they are often followed differently than how the Rabbinates follow them. Two other major differences between Rabbinates and Karaites involve tefillin and mezuzot and familial descent. Karaites do not take the passages from Numbers and Deuteronomy literally and as a result do not wear tefillin or place mezuzot upon their doors. Karaites, unlike Rabbinates, follow the Tanakh when it comes to determining familial descent. Karaites maintain that a child is born a Jew only if the father is a Jew – the opposite of Rabbinic Judaism. This is the tradition according to the Tanakh and is therefore the tradition amongst the Karaites.
Karaite Judaism believes that the Torah was given to the Prophet Moses and the entire Tanakh is considered sacred text. Karaites believe that only the Tanakh must be consulted for the determination of how one is to live according to God’s will. (31) 
1Alieza Salzberg. “Judaism after the Temple: Coping with destruction and building for the future.” MyJewishLearning, n.d. [http://www.myjewishlearning.com/history/Ancient_and_Medieval_History/539_BCE-632_CE/Palestine_Under_Roman_Rule/Judaism_after_the_Temple.shtml]
2I. Epstein. “Tractate Gittin.” [http://halakhah.com/pdf/nashim/Gittin.pdf]
3American-Israeli Cooperative Enterprise. “Tradition.” Jewish Virtual Library, 2008. [http://www.jewishvirtuallibrary.org/jsource/judaica/ejud_0002_0020_0_19989.html]
4I. Epstein. “Tractate Berachot.” [http://halakhah.com/pdf/zeraim/Berachoth.pdf]
5I. Epstein. “Tractate Megilah.” [http://halakhah.com/pdf/moed/Megilah.pdf]
6Jacob Neusner. “Rabbinic Judaism: The Theological System.” 2003 [http://www.brill.com/rabbinic-judaism-0]
7Nehemia Gordon. “History of Karaism.” karaite-korner.org. World Karaite Movement, 3 April 2011, accessed 15 April 2012. [http://karaite-korner.org/history.shtml]
8David Stein (ed.). JPS Hebrew-English Tanakh. Philadelphia: Jewish Publication Society, 1999.
9William Whiston (trans.). “The Works of Flavius Josephus.” (1737) 13:5:9. [http://www.sacred-texts.com/jud/josephus/index.htm#aoj]