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What do Jews believe?
Abraham Joshua Heschel, Moral Grandeur and Spiritual Audacity, "Jewish Theology"
...[The] atmosphere in which I grew up was full of theology. Day and night we spoke only about "prayer" and kavanah (undivided concentration, particularly in prayer) and about Hakodesh Baruch Hu (the Holy One, blessed be He), and about mesirat nefesh (extreme devotion; literally, "giving over one's soul"). What is this? It is Jewish theology....Erev Yom Kippur was my great day of training in Jewish theology, because we knew what the problem was: "Do I have the right to survive the year without tshuvah (repentance, literally 'return')?" It was actually living theology. Vehayu hayecha tluim lecha mineged (And your life shall hang in doubt before you--Deuteronomy 28:66). This was not merely performance (as I have often seen and observed) or what I call "religious behaviorism."

(א) ...נגד מה ה' דורש ממך אמר והצנע לכת עם אלקיך, מה שאתה צריך ללכת עם אלקיך (כמו את האלקים התהלך נח), שזה שורש המצות שבין אדם למקום שילך עם אלקים, ללכת בדרכיו ולהתקדש בקדושתו, כמ"ש והייתם קדושים כי קדוש אני, זה יהיה בהצנע ובסתר, כי הם דברים שבינך ובין קונך ובזה טובה הצניעות בל יזיד וירים לבו בעניני החקירה באלהות וכן בל יתחכם על מצותיו, רק ילך בהצנע לכת עם אלקים:

...As to [the question], What does God require from you?, it says: And walking modestly with your God - that you must walk with your God (as in [the verse] And Noakh walked along with God [Breishit 6:9]). This is the root of the mitzvot between humankind and the Omnipresent - to walk with God, to walk in His paths and to make oneself holy with His holiness, as it is written: And You shall be holy for I am holy [Vayiqra 11:44]. This should be in modesty and secrecy, for these are things between you and your Maker. And in this, modesty is best, lest one overstep and become haughty [lit., raise one's heart] in the matters of inquiring into the Divine, and similarly lest one make oneself [too] wise about His mitzvot. One should simply walk modestly, walking with God.

(א) יְסוֹד הַיְסוֹדוֹת וְעַמּוּד הַחָכְמוֹת לֵידַע שֶׁיֵּשׁ שָׁם מָצוּי רִאשׁוֹן. וְהוּא מַמְצִיא כָּל נִמְצָא. וְכָל הַנִּמְצָאִים מִשָּׁמַיִם וָאָרֶץ וּמַה שֶּׁבֵּינֵיהֶם לֹא נִמְצְאוּ אֶלָּא מֵאֲמִתַּת הִמָּצְאוֹ:

(1) The foundation of foundations, and the pillar of wisdoms, is to know that there is a first Being, and that He causes all other beings to be; and that all things existing from heaven to earth, and whatever is between them, exist only through the verity of His existence.

(א) היא הצווי אשר צונו בהאמנת האלהות, והוא שנאמין שיש שם עלה וסבה הוא פועל לכל הנמצאים, והוא אמרו אנכי ה' אלקיך. ובסוף גמרא מכות (דף כ"ג:) אמרו תרי"ג מצות נאמרו למשה בסיני, מאי קראה תורה צוה לנו משה, ר"ל מנין תור"ה. והקשו על זה ואמרו תורה בגימטריא תרי"א הוי, והיה המענה אנכי ולא יהיה מפי הגבורה שמענום. הנה נתבאר לך שאנכי ה' מכלל תרי"ג מצות, והוא צווי באמונת האלהות...

...This is the commandment through which we were commanded concerning the belief in the Divine. And it is that we should believe that there is a One above, and that He is the cause and enactor of all that is real, and that is what it is said: "I am Ha-shem your God." [Shmot 20:2]. And at the end of the gemara Makot (23b), they said: 613 [taryag] mitzvot were said to Moshe at Sinai. What text [proves this]? "Moshe commanded the torah to us." [Dvarim 33:4] This means to say, [he commanded] the total numerical equivalent of [the letters] T-O-R-H. And they questioned this, and said that Torah in gematria is 611, and the riposte was: [The utterances] "I am..." and "There shall be no..." [i.e., the first two of the Ten Sayings/ 'Aseret ha-Dibrot], those we heard from the mouth of Divine Majesty. Here it is explained to you that "I am Ha-shem" is included among the 613 mitzvot, and it is the commandment for belief in the Divine...

Rabbi Jonathan Sacks, "Covenant and Conversation, Va-etchanan 5775
Available at: http://rabbisacks.org/the-right-and-the-good-vaetchanan-5775/
This... is the difference between the God of Aristotle and the God of Abraham. Aristotle thought that God knew only universals not particulars. This is the God of science, of the Enlightenment, of Spinoza. The God of Abraham is the God who relates to us in our singularity, in what makes us different from others as well as what makes us the same.
This ultimately is the difference between the two great principles of Judaic ethics: justice and love. Justice is universal. It treats all people alike, rich and poor, powerful and powerless, making no distinctions on the basis of colour or class. But love is particular. A parent loves his or her children for what makes them each unique. The moral life is a combination of both. That is why it cannot be reduced solely to universal laws. That is what the Torah means when it speaks of “the right and the good” over and above the commandments, statutes and testimonies (Dvarim 6:17-18).

(א) והאמן בה' ויחשבה לו צדקה פירש רש"י הקדוש ברוך הוא חשב לו צדקה וזכות על האמונה שהאמין בו ואיני מבין מה הזכות הזאת למה לא יאמין באלקי אמן והוא הנביא בעצמו ולא איש קל ויכזב ומי שהאמין לשחוט את בנו היחיד האהוב ושאר הנסיונות איך לא יאמין בבשורה טובה והנכון בעיני כי יאמר שהאמין בה' וחשב כי בצדקו של הקב"ה יתן לו זרע על כל פנים לא בצדקת אברם ובשכרו אף על פי שאמר לו "שכרך הרבה מאד" ומעתה לא יירא פן יגרום החטא ואף על פי שבנבואה הראשונה חשב שתהיה על תנאי כפי שכר מעשיו עתה כיון שהבטיחו שלא יירא מן החטא ויתן לו זרע האמין כי נכון הדבר מעם האלקים אמת לא ישוב ממנה כי צדקת ה' היא ואין לה הפסק כענין שכתוב (ישעיהו מה כג) בי נשבעתי נאם ה' יצא מפי צדקה דבר ולא ישוב ...

...And he believed in God and thought it to be righteousness on his part. Rashi expounded: The Holy One (blessed be He) thought it to be righteousness and merit on his part, in the belief that he believed in Him.

And I don't understand what this merit is, why wouldn't he believe in a caring God? And he himself was a prophet! And God is not a human to deal faithlessly [B-Midbar 23:19]! And someone who believes [so far as] to slaughter his only and beloved son, and all the rest of the trials - how would he not believe in good news?

And what is correct in my eyes is that when it says that he believed in God, he thought that it was through the righteousness of the Holy One (blessed be He) that He would give him offspring. In any case, [it would not depend] on Avram's righteousness and his reward, even though He said to him, Your reward is very great. And henceforth he would not fear lest sin intervene [to disentitle him]. And even though in the first prophecy he thought that [God's promise] would be on condition as a reward for his actions, now - since He has promised him that he need not fear sin and He will give him offspring - he believed that the matter was established from the God of truth who would not resile from it, for that is God's righteousness and it never ceases, as in the matter where it is written: By Myself have I sworn - the word of God - righteousness comes out of My mouth, a word that will not be turned back. (Yeshayahu 45:23)

(א) משֶׁה קִבֵּל תּוֹרָה מִסִּינַי, וּמְסָרָהּ לִיהוֹשֻׁעַ, וִיהוֹשֻׁעַ לִזְקֵנִים, וּזְקֵנִים לִנְבִיאִים, וּנְבִיאִים מְסָרוּהָ לְאַנְשֵׁי כְנֶסֶת הַגְּדוֹלָה. הֵם אָמְרוּ שְׁלשָׁה דְבָרִים, הֱווּ מְתוּנִים בַּדִּין, וְהַעֲמִידוּ תַלְמִידִים הַרְבֵּה, וַעֲשׂוּ סְיָג לַתּוֹרָה:

(1) Moshe received the Torah from Sinai and transmitted it to Yehoshua, and Yehoshua to the Elders, and the Elders to the Prophets, and the Prophets transmitted it to the Men of the Great Assembly. They said three things: Be deliberate in judgment, set up many students and make a fence for the Torah.

The Essential Talmud, Adin Steinsaltz (transl. Chaya Galai), "The Talmud's Importance for the People"
...Talmudic scholarship is to a certain extent self-contradictory, a type of "sacred intellectualism"....[It] is not regarded merely as a secular exercise in developing the mind or abstract capacity for thought, but as a subject of intrinsic sanctity. The questioning, searching, and skeptical man is not excluded from the circle of believers; he becomes, rather, the spokesman of the central work of the Jewish religion, the prime source for halakhah and daily conduct. This very process creates the unique blend of profound faith and questioning skepticism that has characterized the Jewish people throughout the ages. Incessant self-criticism, together with the constant awareness that beyond it lies a reality to which one must adhere, is a central theme of Jewish existence.
Further reading:
​Pirke Avot
Faith: A Jewish Approach, Louis Jacobs, 1968 - Website: louisjacobs.org
The Essential Talmud, Adin Steinsaltz (transl. Chaya Galai), 1976
The Limits of Orthodox Theology: Maimonides' Thirteen Principles Reappraised, Marc Shapiro, 2004
Must a Jew Believe Anything?, Menachem Marc Kuttner, 2006
Website: http://people.ucalgary.ca/~elsegal/TalmudPage.html

(א) יִגְדַּל אֱלקִים חַי וְיִשְׁתַּבַּח, נִמְצָא וְאֵין עֵת אֶל מְצִיאוּתו. אֶחָד וְאֵין יָחִיד כְּיִחוּדו, נֶעְלָם וְגַם אֵין סוף לְאַחְדוּתו. אֵין לו דְמוּת הַגּוּף וְאֵינו גוּף, לא נַעֲרךְ אֵלָיו קְדֻשָּׁתו. קַדְמון לְכָל דָּבָר אֲשֶׁר נִבְרָא, רִאשׁון וְאֵין רֵאשִׁית לְרֵאשִׁיתו. הִנּו אֲדון עולָם לְכָל נוצָר, יורֶה גְדֻלָּתו וּמַלְכוּתו. שֶׁפַע נְבוּאָתו נְתָנו, אֶל אַנְשֵׁי סְגֻלָּתו וְתִפְאַרְתּו. לא קָם בְּיִשרָאֵל כְּמשֶׁה עוד, נָבִיא וּמַבִּיט אֶת תְּמוּנָתו. תּורַת אֱמֶת נָתַן לְעַמּו אֵ-ל, עַל יַד נְבִיאו נֶאֱמַן בֵּיתו. לא יַחֲלִיף הָאֵ-ל וְלא יָמִיר דָּתו, לְעולָמִים לְזוּלָתו. צופֶה וְיודֵעַ סְתָרֵינוּ, מַבִּיט לְסוף דָּבָר בְְַּקַדְמָתו. גּומֵל לְאִישׁ חֶסֶד כְּמִפְעָלו, נותֵן לְרָשָׁע רַע כְּרִשְׁעָתו. יִשְׁלַח לְקֵץ הַיָּמִין מְשִׁיחֵנוּ, לִפְדּות מְחַכֵּי קֵץ יְשׁוּעָתו. מֵתִים יְחַיֶּה אֵ-ל בְּרב חַסְדּו, בָּרוּךְ עֲדֵי עַד שֵׁם תְּהִלָּתו:

[Piyut based on the Thirteen Principles of Faith established by Rambam]

1. May the living God grow great, and be praised, He exists and there is no fixed time for His existence.

2. He is one, and there is no unity like His; He is concealed and also his singularity is endless.

3. He has no bodily form nor substance; His holiness has no comparison.

4. He preceded all that was created, [He is] the first and there was none begun before His beginning.

5. See, He is the lord of the world for every creature, which shows His greatness and majesty.

6. An abundance of prophecy, He gave to His chosen and splendorous people.

7. There has never again arisen in Israel another like Moshe, prophet and one who gazed upon His image.

8. God gave to His people a true Torah, by the hand of His prophet, the most faithful in His house.

9. God will not alter, nor will He change His mind, forever for a counterpart.

10. He looks out and sees our secrets, gazing at the end of a matter in its beginning.

11. He deals with a kindly person according to their actions, and gives evil to the wicked according to their wickedness.

12. At the end of days, He will send our anointed, to redeem those who wait for the conclusion of His salvation.

13. God will revive the dead, in His abundant kindness, blessed be His praised name forever.