The source for the following summary of each of these thirteen principles is Maimonides' introduction to the tenth chapter of the Mishnaic tractate, Sanhedrin.
The existence of the world or any part of it is dependent upon the existence of the single, unique Creator. But the existence of this Creator, the Master of the universe, is not dependent on anything.
This principle is known as "Yichud" -- G-d's Oneness. There is only one G-d. He is unique, and is without any divisions. There is nothing in the universe with which we can compare His Oneness. This aspect of G-d's existence is clear from the verse "Hear, oh Israel, G-d is our Lord, G-d is one." (Deut. 6 4).
G-d has no body or any physical aspect, nor is His Power that of a physical body. This principle builds on the logic of the previous one. If G-d were to have a body, it would limit Him to the confines of that body, and therefore He would not be infinite and incomparable in the same way. There are many places in the Bible where G-d is described as "stretching out His hand" (or doing some similar physical action). These are only figures of speech (anthropomorphisms). They are sublime actions couched in words that humans can understand.
G-d has always existed and always will. He is eternal. Again, if this weren't true, and G-d would be limited (by time) and he would no longer be "infinite."
Idolatry: There is no individual or power besides G-d whom it is fitting to worship or serve. Even to worship (or attribute independent power to) intermediaries (like angels, other human beings, stars or planets) is forbidden. Such worship is in the category of idolatry. G-d created the universe and every single one of its parts, it is to Him that we owe all of our gratitude and subservience.
The sixth principle of the Rambam is "Nevu'a" - prophecy. G-d grants prophecy to people who have perfected their personal character and who follow all the commandments of the Torah. Prophecy does not come to unlearned and unprepared people.
The prophecy of our teacher Moses (through whom the Torah was transmitted at Mt Sinai) was greater than all other prophecy in four ways:
It was not "heard" through any intermediary (i.e. an angel, a cloudy vision) but was directly from G-d.
It was always given while Moshe was wide awake, in complete control of his faculties.
Moshe was not overcome with shaking and dread as were other prophets, but was calm and alert.
Moshe had the incredible ability to summon prophecy at will. Other prophets had to prepare and wait until G-d chose to appear.
The giving of the Torah: The words of the Written Torah (the "Five Books of Moses") are the true and completely accurate words of G-d. The words in the Torah were dictated by G-d to Moshe. In essence, the verse "Shema Yisroel..." - (Hear O Israel...) is just as meaningful to us as the lists of names and places written in the Torah. They all come from G-d and there is great, limitless wisdom to be found in every word. G-d also taught Moshe how to carry out the commandments found in the Written Torah; these G-d-given explanations form part of what we call the Oral Torah.
Since the entire Torah comes from G-d, one may not add to it or subtract from it (i.e. add or subtract commandments. For instance to say that there is no commandment of Tefillin...).
G-d is aware of all our actions and does not ignore them.
The Messiah (lit "anointed one"), a descendant of King David, will come, and could come at any time. He will be wiser than King Soloman and possess a level of prophecy close to that of Moses.
There will eventually be a revival of the dead.
Rabbi Boruch Clinton teaches at the Ottawa Torah Institute yeshiva high
school and Machon Sarah high school for girls (both in Ottawa, Canada).
You may reach him with comments and questions at