The foundations of the Torah rest on three pillars: the existence of God, reward and punishment, and the fact that the Torah is from Heaven.

In my opinion, the correct way to count the principles that compose the foundation of the divine Torah is this: There are a total of three general principles that are necessary for the true religion, and they are: the existence of God, providence with regard to reward and punishment, and Torah from Heaven. (Rav Yosef Albo, Sefer HaIkkarim 1:4)

The Torah rests on six foundations: God knows what happens to His creations, watches over them, is omnipotent, and grants prophecy to the prophets, free will to human beings, and purpose to the world.

There are foundations and pillars that support the house of God, and whose reality make possible the truth of the Torah to be ordered by Him, may He be blessed. If one of them were missing, the [truth of] the entire Torah would collapse, God forbid. When we investigated, we found that these are six: (1) God’s knowledge of reality, (2) His providence over it, (3) His power, (4) prophecy [which He gives to human beings], (5) free will, and (6) the purpose [of the Torah and the world, which is realized through humankind]. (Rav Ĥasdai Crescas, Or Hashem 2:1)

There are thirteen principles of Judaism, which constitute the specifics derived from three foundations: faith in God, His connection to human beings, and reward and punishment.

The foundations of faith in God:

There are thirteen principles, or foundations, of our religion: (1) The existence of the Creator, namely, a Being who is perfect in all ways. He is the cause of the existence of all creatures; their reality is dependent upon Him and derives from Him…. (2) The oneness of God, meaning that He, who is the cause of everything, is one…. (3) His incorporeity: He is not a material body, nor a physical force. Features of physicality, like movement and being at rest, do not apply to Him, either in essence or incidentally…. (4) Eternity: He is eternal and nothing besides him is eternal as He is. Know that the great foundation in the Torah of Moses, our teacher, is that the world is created. God created it ex nihilo…. (5) God is the One whom it is fitting to serve and extol, to proclaim His greatness and perform His mitzvot. And one should not do these for anything whose existence is inferior to His.

The foundations of God’s connection with humankind:

(6) Prophecy: One should know that in humankind there are those with a nature composed of exceptionally pure and elevated character traits and great perfections, whose souls are prepared…. These are the prophets, and this is prophecy, and that is what it concerns.… (7) The prophecy of Moses our teacher: We must believe that he was the father of all the prophets who came before him, as well as those who arose after him. All were on a level inferior to his.… (8) The Torah is from Heaven: We must believe that the entire Torah that we have today is the one given through Moses, the entirety of which came from the mouth of the Almighty.… (9) Abrogation: The Torah of Moses will not be revised or replaced, and no other Torah will ever come from the Creator. One must not add to it nor subtract from it. This refers to both the Written Torah and the Oral Torah.

The foundations of reward and punishment:

(10) God knows the deeds of human beings and does not ignore them.… (11) God rewards a person who fulfills the mitzvot of the Torah, and He punishes whoever violates the Torah’s prohibitions. The greatest reward is the World to Come, and the harshest punishment is excision from the World to Come.… (12) The messianic era: Believing and trusting that the anointed one will come, and do not think that he will be late: “If it [the end of days] tarries, wait for it” (Habakkuk 2:3). (13) The revival of the dead. (Rambam, Commentary on the Mishna, Sanhedrin 10:1)

Further reading: For more on prophecy, see p. 203; for more on the Torah being from Heaven, see p. 269; for more on divine providence, see p. 173; for more on reward and punishment, see p. 256; for more on the messianic era, see p. 145; for more on the revival of the dead, see p. 295.