This is a difficult question because
Judaism has many sects and within each sect there are many gray areas. This is because every community has their own rabbi that they choose to follow.
1. Reconstructionist Judaism - Started by Mordechai Kaplan in the early 1900's. It focuses more on the values and traditions of Judaism, does not require a belief in God and rejects the tradition that Jews are a chosen people.
2. Reform Judaism - Started by Rabbi Isaac Mayer Wise in the late 1800's. Reform Jews believe in God, zionism and divine inspiration of the Torah. They are accepting of homosexuality, promote the same religious roles for men and women and have a looser definition for what constitutes a Jew.
3. Conservative Judaism - Founded by Rabbi Zecharial Frankel in the mid 1800's. They believe in God, the divinity of the Torah and zionism and place an importance on traditional Jewish laws. However they believe in pluralism in Judaism and different congregations can accept different rulings, while still being considered part of religious Judaism. They also recognize human influence in religious texts and see them as religious as well as historical documents.
4. Karaites - These Jews believe only in the written law, not the oral tradition.
5. Orthodox Judaism - This, the original branch of Judaism, believes in God, the divinity of the Torah, and strictly adheres to the traditional laws. They fully accept religious tradition while still interacting in the modern world. Because of this broad definition, individuals who consider themselves orthodox vary in terms of their amount of Torah study (ranging from no studying to studying as a part time job), dress (street clothes vs. always wearing a formal white button down shirt and black suit pants) and minor differences in interpretations of Jewish law (ex: women are not allowed to wear the clothes of a man. So do pants count as men's clothes? where do you draw the line?)
6. Hasidic Judaism - This branch of Judaism is identified as being the most stringent because of their dress. This is a branch of orthodox Judaism that emphasizes singing, dancing and mysticism together with keeping the Torah. It was founded in the 1700's by the Rabbi Baal Shem Tov. They dress as they do in order to mimic the fashion of the rabbis whose teachings they follow.
Just a note, the terms Sephardic and Ashkenazi refer to the person's geographical origin more than their religious belief.
Religious Judaism is based on a written and oral tradition. The written law, the Torah, was transcribed by Moses on Mount Sinai by the divine will of God. It chronicles the beginning of creation up until the Jews entering the land of
Israel. The oral law was also given to Moses on Mount Sinai (which was eventually transcribed by Rabbi Judah in 190 C.E in a book called the Mishnah) and it elaborates on the commandments present in the Torah. The rest of the Talmud (containing the Mishna) is essentially a written record of rabbinical analysis and commentary on the laws in the Mishnah. As modern society progresses, Judaism is constantly keeping in pace by extrapolating laws from ancient texts to apply to modern day situations (for example, creating a fire is not allowed on the Sabbath, so what about starting a car engine?). In ancient Israel these laws were decided in a high court of law called the Sanhedrin which ceased due to persecution around 400 C.E. and can only be reinstated if all the Rabbinic leaders were to agree on one person who is qualified to reinstate the Sanhedrin. Even if this ruling body were to exist it would not be able to change existing Jewish laws. This is because changing a Jewish law can only be done by a Sanhedrin that is greater than the preceding one. Therefore, even though today we know science that might challenge the basis for certain Jewish rulings, they can not be removed. New Jewish laws, however, can be made by contemporary Rabbis who have enough recognition and popularity in the Jewish community.
The philosophy of Judaism is that this world is a purposeful creation by God, in which all people are tested concerning their use of free-will. We possess a soul which lives on after the body dies and is held responsible for the person's actions. Anyone who is worthy, Jewish or not, can merit reward in the afterlife.
Here is a list of the most basic beliefs of Judaism, as collated by Maimonides:
1. God exists, and is the Creator.
2. God is One and unique.
3. God is not physical.
4. God is eternal.
5. Prayer is to be directed only to God.
6. The words of the prophets are true.
The prophecies of the
Hebrew Bible have been coming true throughout history. Even secular archaeologists (the unbiased ones) have stated that the Hebrew Bible is the most accurate of historical records, as the disdainful theories of Wellhausen and Bible-critics of his ilk have been shattered by the archaeologist's spade. A list of Bible verses which were deemed anachronistic but later shown to be perfectly accurate would run into the many hundreds.
7. The prophecies of Moses are true; and he was the greatest prophet.
8. The Torah was given to Moses by God.
9. There will be no other Torah.
10. God knows the thoughts and deeds of all.
11. God rewards the good and punishes the wicked.
12. The Messiah will come.
13. The dead will be resurrected.