What are the central beliefs of Judaism?

Beliefs in God, education justice and obedience

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.

• Link: Judaism and philosophy
  
• Link: The Creation
  

Here is a list of the most basic beliefs of Judaism, as collated by Maimonides:
1. God exists, and is the Creator.
This tells us that the world is not purposeless or chaotic. Life is the result of a deliberate, purposeful, intelligent and kind Creator; not a melancholy chaos or a string of fortuitous accidents.

• Link: Can you show that God exists
  

2. God is One and unique.
This is the basis of all Western monotheistic belief, which was given to the world by Abraham and his descendants. This belief places God at the center of reality and of our world-outlook and thoughts.

• Link: Biography of Abraham
  

3. God is not physical.

• Link: What do Jews believe God is like?
  

This includes the corollary that no person should be worshiped as God or as a god. Judaism has no god-kings, no demigods, no angel who flouts God's will, and no sports-idols, movie-idols etc.

4. God is eternal.
This includes the belief that God's ways are also eternal. God is not capricious, forgetful or fickle. Investing in a relationship with God is the only thing that will bear eternal benefits.

5. Prayer is to be directed only to God.
This also teaches us that no person, government or institution is to be accorded blind trust. We pray directly to God, three times a day; and we recount our shortcomings, ask for our needs, and acknowledge our successes with happy thanks.

6. The words of the prophets are true.

• Link: About the Hebrew Prophets
  

• Link: Refuting theories of Bible-critics
  

8. The Torah was given to Moses by God.
These two beliefs are the basis of our attitude towards the Torah: it is the center of our lives. Jews are keeping mitzvot (commands), saying blessings, praying, learning Torah and doing acts of kindness and charity all the time. The Torah is the single greatest thing that a Jew has; given to us to provide knowledge, guidance, inspiration, awe and reverence, advice, law, comfort, history and more. It is the basis of Judaism.

9. There will be no other Torah.
We Jews have been around for 3800 years. New fads, manifestos, beliefs or lifestyles which rear their heads are met by the Jew with a calm, seasoned eye and the proverbial grain of salt. The Torah doesn't change; and every new thing can be measured against the Torah's standards.

10. God knows the thoughts and deeds of all.
11. God rewards the good and punishes the wicked.
These two beliefs provide a vast incentive towards righteousness and, when needed, repentance.
They also form part of the basis of our belief in the afterlife, since this entire world wouldn't be enough to reward a Moses or punish a Hitler.
God is just (Deuteronomy 32:4); and all outstanding accounts are settled after this life.

12. The Messiah will come.
13. The dead will be resurrected.

• Link: The afterlife in Judaism
  

Judaism is the only ancient religion which taught optimism; and a large part of that optimism was and is based upon the words of the prophets.