Hebrews

Israelites

Judean

• was a member of the Tribe of of Judah, or
• lived in Judea

I.e., all members of the Tribe of Judah were Israelites, but not all Israelites were Judeans. Not all who lived in Judea were practitioners of the Old Testament religion or were of the Tribe of Judah. Judah is a subset of ancient Israel, not a synonym for it.
 

Jew

• per a religious standard, anyone who practices Judaism (the modern name for rabbinic Talmudism)
• per the Talmud and other racist standards, such as Nazism, anyone whose mother is a Jew (which begs the question)
• per eretz Israel's "Law of Return," someone whose mother is a Jew and who does not practice a religion other than Judaism (i.e., a "Jew" can be an atheist and can still be called a "Jew") or someone who converts to Judaism
• after the Babylonian Captivity: those of the blended House of Judah (members of the Tribes of Juda, Levi, and Benjamin)
• per the New Testament, all Christians (Romans 2:28-29)

Israel

• The people of God. In Old Testament times, these were the Hebrews and converted "strangers" (those of other nations) who honored the Covenant made through Abraham's son, Jacob. It was after Jacob was renamed "Israel" that the faithful came to be known as "Israelites."
  
  In the Church age, it refers to all those who honor the New Covenant in Jesus Christ. That line from Adam to Christ, the New Adam, is straight: the tree of Israel is and will always be one tree, with some branches broken off and some grafted in.
   
• a political state more properly and fully called "Eretz Israel," and whose inhabitants are called "Israelis" -- most of whom are ethnic Jews, many of whom are not (note, too, that not all Palestinians are Muslims; many are Christians, for example), and most of whom do not practice Judaism (neither the Old Testament religion nor Talmudism). After the Temple fell in 70 A.D., the land now known as Israel was named by the Romans "Palestine."

Judaism

• Mishnah:
  (230 A.D.) Originally Oral Law, but written down in 200 A.D.The Mishnah consists of:
  • Zera'im ("Seeds"): 11 tractates on crops, foods, and land-related regulations
  • Mo'ed ("Festivals"): 12 tractates on the Sabbath and the liturgical year
  • Nashim ("Women"): 7 tractates on marriage, divorce, and oaths
  • Neziqin ("Torts"): 10 tractates on criminal and civil law
  • Qodashim ("Sacred Things"): 11 tractates about sacrifices and the Temple
  • Tohorot ("Purity"): 12 tractates about purity laws and rituals
    
    
• Yerushalmi or "Palestinian Talmud":
  (400 A.D.)
  
  
• Midrash:
  (ca 400-500 A.D.) Consists of sermons, Biblical commentary, parables, etc.
  
  
• Bavli or the "Babylonian Talmud":
  (compiled ca. 430-560 A.D.) Contains around half of the Mishnah and commentary called Gemara (the word "Gemara" is often used interchangeably with "Talmud"). It is the Babylonian Talmud that is most often referred to when one speaks of "the Talmud." This is the most important literature in modern Judaism, even more important than Torah.
  
  
• Kabbalah:
  (codified ca early 14th c.) Claimed to be a part of Torah given to Adam, the Kabbalah (the word means "tradition") is a mystical system that concerns itself with the process of creation. Because of its esoteric, gnostic elitist nature and its emphasis on magic, the conjuring of supernatural forces, numerology, astrology, reincarnation, etc., watered-down Kabbalah has become a trendy, New Age fashion.
  
  True Kabbalah, however, is for initiates and is not supposed to be studied until one is firmly grounded in basic Judaic principles (usually around the age of 40 among the non-Hassidic). Parts of Kabbalah are in print (the Zohar --"Book of Splendor"-- by Moses de Leon, for example), but other parts are a matter of orally transmitted, deeply secret tradition. Kabbalah has played a great role in the development of many diverse movements, including Masonry, Rosicrucianism, Renaissance-era secular and Christian thought, Aleister Crowley's Hermetic Order of the Golden Dawn (and other Hermetic systems), and Mormonism.
  
  
• Tosefta:
  (12th c.) another compilation of Oral Law, like the Mishnah, but treated with less authority and as a supplement, a practical guide to the Mishnah

The rabbi is not the equivalent of the Israelite priest, for they offer no sacrifices and the Temple is no more. The equivalent of the Israelite priest is the Catholic priest who is ordained after the order of Melchizedek and who re-presents the once and for all Sacrifice of Christ on Calvary.
 

Jewish subcultures

• Ashkenazi Jews:
  the Central and Eastern European Jews. Most of the Eastern European Jews are descended from the Turkish Kingdom of Khazaria (an area of land known to the Greeks as "Scythia"; to the Church Fathers as "Magog"; and to moderns as various Eastern European and Southern Russian States) which converted to Judaism in the 8th and 9th centuries. The vast majority of modern Jews fall into this category. The Jewish historian, Josephus, writes that the people of this area descended genetically from Japheth, son of Noah and brother of Shem, the father of the Semites. Shem's descendant, Eber, gave his name to the Hebrews.)
  
  
• Sephardic Jews:
  Jews who settled in the Mediterranean area and are mostly associated with Spain.
  
  
• Arab and Yemenite Jews:
  Jews who descend from a Jewish kingdom in Yemen in the early Middle Ages under the rule of Dhu Nuwas
  
  
• Ethiopian Jews:
  African Jews who claim origin from the Tribe of Dan
  
  
• Karaite Jews:
  Sect, begun in the 8th century, that rejects rabbinical authority

There are also Jews of many "races," as it were, in other parts of Africa, China, India, and other places.