Angels in Judaism

(ז) אֱלוֹהַּ זֶה אֶחָד הוּא וְאֵינוֹ שְׁנַיִם וְלֹא יֶתֶר עַל שְׁנַיִם. אֶלָּא אֶחָד. שֶׁאֵין כְּיִחוּדוֹ אֶחָד מִן הָאֲחָדִים הַנִּמְצָאִים בָּעוֹלָם. לֹא אֶחָד כְּמִין שֶׁהוּא כּוֹלֵל אֲחָדִים הַרְבֵּה. וְלֹא אֶחָד כְּגוּף שֶׁהוּא נֶחְלָק לְמַחְלָקוֹת וְלִקְצָווֹת. אֶלָּא יִחוּד שֶׁאֵין יִחוּד אַחֵר כְּמוֹתוֹ בָּעוֹלָם. אִלּוּ הָיוּ אֱלֹהוּת הַרְבֵּה הָיוּ גּוּפִין וּגְוִיּוֹת. מִפְּנֵי שֶׁאֵין הַנִּמְנִים הַשָּׁוִין בִּמְצִיאוּתָן נִפְרָדִין זֶה מִזֶּה אֶלָּא בִּמְאֹרָעִין שֶׁיֶּאֶרְעוּ בַּגּוּפוֹת וְהַגְּוִיּוֹת. וְאִלּוּ הָיָה הַיּוֹצֵר גּוּף וּגְוִיָּה הָיָה לוֹ קֵץ וְתַכְלִית שֶׁאִי אֶפְשָׁר לִהְיוֹת גּוּף שֶׁאֵין לוֹ קֵץ. וְכָל שֶׁיֵּשׁ לְגוּפוֹ קֵץ וְתַכְלִית יֵשׁ לְכֹחוֹ קֵץ וָסוֹף. וֵאלֹהֵינוּ בָּרוּךְ שְׁמוֹ הוֹאִיל וְכֹחוֹ אֵין לוֹ קֵץ וְאֵינוֹ פּוֹסֵק שֶׁהֲרֵי הַגַּלְגַּל סוֹבֵב תָּמִיד. אֵין כֹּחוֹ כֹּחַ גּוּף. וְהוֹאִיל וְאֵינוֹ גּוּף לֹא יֶאֶרְעוּ לוֹ מְאֹרְעוֹת הַגּוּפוֹת כְּדֵי שֶׁיְּהֵא נֶחְלָק וְנִפְרָד מֵאַחֵר. לְפִיכָךְ אִי אֶפְשָׁר שֶׁיִּהְיֶה אֶלָּא אֶחָד. וִידִיעַת דָּבָר זֶה מִצְוַת עֲשֵׂה שֶׁנֶּאֱמַר (דברים ו ד) "ה' אֱלֹהֵינוּ ה' אֶחָד":

Mishneh Torah, Foundations of the Torah 1:7

(7) This G-d is one. He is not two or more, but one, unified in a manner which [surpasses] any unity that is found in the world; i.e., He is not one in the manner of a general category which includes many individual entities, nor one in the way that the body is divided into different portions and dimensions. Rather, He is unified, and there exists no unity similar to His in this world.
If there were many gods, they would have body and form, because like entities are separated from each other only through the circumstances associated with body and form.
Were the Creator to have body and form, He would have limitation and definition, because it is impossible for a body not to be limited. And any entity which itself is limited and defined [possesses] only limited and defined power. Since our God, blessed be His name, possesses unlimited power, as evidenced by the continuous revolution of the sphere, we see that His power is not the power of a body. Since He is not a body, the circumstances associated with bodies that produce division and separation are not relevant to Him. Therefore, it is impossible for Him to be anything other than one.
The knowledge of this concept fulfills a positive commandment, as [implied by Deuteronomy 6:4]: "[Hear, Israel,] God is our Lord, God is one."

חגיגה י״ד א:ג׳

אֲמַר לֵיהּ שְׁמוּאֵל לְחִיָּיא בַּר רַב: בַּר אַרְיָא! תָּא אֵימָא לָךְ מִילְּתָא מֵהָנֵי מִילֵּי מְעַלְּיָיתָא דַּהֲוָה אָמַר אֲבוּךְ: כֹּל יוֹמָא וְיוֹמָא נִבְרָאִין מַלְאֲכֵי הַשָּׁרֵת מִנְּהַר דִּינוּר, וְאָמְרִי שִׁירָה וּבָטְלִי, שֶׁנֶּאֱמַר: ״חֲדָשִׁים לַבְּקָרִים רַבָּה אֱמוּנָתֶךָ״. וּפְלִיגָא דְּרַבִּי שְׁמוּאֵל בַּר נַחְמָנִי. דְּאָמַר רַבִּי שְׁמוּאֵל בַּר נַחְמָנִי אָמַר רַבִּי יוֹנָתָן: כׇּל דִּיבּוּר וְדִיבּוּר שֶׁיּוֹצֵא מִפִּי הַקָּדוֹשׁ בָּרוּךְ הוּא נִבְרָא מִמֶּנּוּ מַלְאָךְ אֶחָד, שֶׁנֶּאֱמַר: ״בִּדְבַר ה׳ שָׁמַיִם נַעֲשׂוּ וּבְרוּחַ פִּיו כׇּל צְבָאָם״.

Chagigah 14a:3

Shmuel said to Ḥiyya bar Rav: Son of great ones, come and I will tell you something of the great things that your father would say: Each and every day, ministering angels are created from the River Dinur, and they recite song to G-d and then immediately cease to exist, as it is stated: “They are new every morning; great is Your faithfulness” (Lamentations 3:23), indicating that new angels praise G-d each morning. The Gemara comments: And this opinion disagrees with that of Rabbi Shmuel bar Naḥmani, as Rabbi Shmuel bar Naḥmani said that Rabbi Yonatan said: With each and every word that emerges from the mouth of the Holy One, Blessed be He, an angel is created, as it is stated: “By the word of the Lord the heavens were made, and by the breath of His mouth all their hosts” (Psalms 33:6). The hosts of heaven are the angels, who, he claims, are created from the mouth of G-d, rather than from the River Dinur.

מדרש תנחומא, משפטים י״ט

(א) ‎הִנֵּה אָנֹכִי שֹׁלֵחַ מַלְאָךְ. זֶה שֶׁאָמַר הַכָּתוּב: כִּי מַלְאָכָיו יְצַוֶּה לָּךְ לִשְׁמָרְךָ בְּכָל דְּרָכֶיךָ (תהלים צא, יא). עָשָׂה אָדָם מִצְוָה אַחַת, מוֹסְרִים לוֹ מַלְאָךְ אֶחָד. עָשָׂה שְׁתֵּי מִצְוֹת, מוֹסְרִין לוֹ שְׁנֵי מַלְאָכִים. עָשָׂה כָּל הַמִּצְוֹת, מוֹסְרִין לוֹ מַלְאָכִים הַרְבֵּה, שֶׁנֶּאֱמַר: כִּי מַלְאָכָיו יְצַוֶּה לָּךְ. וּמִי הֵן הַמַּלְאָכִים? אֵלּוּ שֶׁמְּשַׁמְּרִים אוֹתוֹ מִן הַמַּזִּיקִין, שֶׁנֶּאֱמַר: יִפֹּל מִצִּדְּךָ אֶלֶף וּרְבָבָה מִימִינֶךָ (תהלים צא, ז). וּמַה הוּא יִפֹּל? שֶׁמַּשְׁלִימִים לוֹ. כָּעִנְיָן שֶׁנֶּאֱמַר בְּדִבְרֵי הַיָּמִים: וּמִמְּנַשֶּׁה נָפְלוּ עַל דָּוִיד (דה״‎א יב כ, כא). וּכְתִיב: בְּלֶכְתּוֹ אֶל צִיקְלַג נָפְלוּ עָלָיו מִמְּנַשֶּׁה (דה״‎א יב, כא).

(ב) וּרְבָבָה מִימִינֶךָ.

Midrash Tanchuma, Mishpatim 19

(1) Behold, I send an angel before thee (Exod. 23:20). Scripture says elsewhere in reference to this verse: For He will give His angels charge over thee, to keep thee in all thy ways (Ps. 91:11). When a man performs one Mitzva one angel is assigned to guard him; when he performs two Mitzvot, two angels are given to him; when he performs all the Mitzvot, many angels are assigned to him, as it is said: For He will give His angels charge over you. Who are these angels? They are the beings who will protect him from demons, as it is said: A thousand may fall at thy side, and ten thousand at thy right hand (ibid., v. 7). )

משנה תורה, הלכות יסודי התורה ב׳:ז׳

(ז) שִׁנּוּי שְׁמוֹת הַמַּלְאָכִים עַל שֵׁם מַעֲלָתָם הוּא. וּלְפִיכָךְ נִקְרָאִים חַיּוֹת הַקֹּדֶשׁ וְהֵם לְמַעְלָה מִן הַכּל וְאוֹפַנִּים וְאֶרְאֶלִּים וְחַשְׁמַלִּים וּשְׂרָפִים וּמַלְאָכִים וֵאלֹהִים וּבְנֵי אֱלֹהִים וּכְרוּבִים וְאִישִׁים. כָּל אֵלּוּ עֲשָׂרָה הַשֵּׁמוֹת שֶׁנִּקְרְאוּ בָּהֶן הַמַּלְאָכִים עַל שֵׁם עֶשֶׂר מַעֲלוֹת שֶׁלָּהֶן הֵן, וּמַעֲלָה שֶׁאֵין לְמַעְלָה מִמֶּנָּה אֶלָּא מַעֲלַת הָאֵל בָּרוּךְ הוּא הִיא מַעֲלַת הַצּוּרָה שֶׁנִּקְרֵאת חַיּוֹת. לְפִיכָךְ נֶאֱמַר בַּנְּבוּאָה שֶׁהֵן תַּחַת כִּסֵּא הַכָּבוֹד. וּמַעֲלָה עֲשִׂירִית הִיא מַעֲלַת הַצּוּרָה שֶׁנִּקְרֵאת אִישִׁים וְהֵם הַמַּלְאָכִים הַמְדַבְּרִים עִם הַנְּבִיאִים וְנִרְאִים לָהֶם בְּמַרְאֵה הַנְּבוּאָה. לְפִיכָךְ נִקְרְאוּ אִישִׁים שֶׁמַּעֲלָתָם קְרוֹבָה לְמַעֲלַת דַּעַת בְּנֵי אָדָם:

Mishneh Torah, Foundations of the Torah 2:7

(7) The different names with which the angels are called reflect their [spiritual] levels. Thus, they are called:
1) The holy chayyot, who are above all the others;
2) the ofanim; 7) the elohim;
3) the er'elim; 8) the sons of the elohim;
4) the chashmalim; 9) the keruvim;
5) the serafim; 10) the ishim.
6) the mal'achim;
These ten names which are used to refer to the angels reflect their ten [different spiritual] levels. The level above which there is no higher level except that of God, blessed be He, is that of the form called chayyot. Therefore, the prophets state that they are below God's throne of glory.
The tenth [and lowest] level is that of the form called ishim. They are the angels who communicate with the prophets and are perceived by them in prophetic visions. Therefore, they are called ishim, (“men”), because their level is close to the level of human knowledge.

How many instances of angels/malachim are you aware of in Tanach?

What is the geamatria of אָמֵן?
What is the gematria of מַלְאָך?

Angels are referred to as “Omdim/standers” in scripture in contrast to “Mehalchim/Walkers” which is used in reference to man. This matter is not a mere play on words, but a description of difference between man and angels. Standing connotes one’s still position, not moving either backwards or forwards. In service of G-d this means that the angels retain an equal form of Divine experience throughout their existence. They never develop a greater or different experience of G-dliness than that which they are capable of naturally handling. However, man is defined as a walker, as walking connotes constant change of position. Man has the ability to exceed his natural limitations of G-dly experience and grow to receive even more than the angels. This power of spiritual walking is only found in souls that are invested in bodies in the physical world. The souls of man as they are found in the spiritual worlds, such as Gan Eden, are also considered “Standers” just like the angels. The ability to expand one’s G-dly experience to levels that are infinitely greater than one’s natural capacity is a result of the investment of one’s G-dly soul into the animal soul and body which are rooted in Tohu and G-d’s essence. It is the Torah and Mitzvos performed in this world in a physical body with Iskafya and Ishapcha that give man the ability to grow beyond the levels of angels or even his own soul as it existed prior to its descent.
(Torah Ohr)

אור החיים על שמות כ׳:ב׳

(א) אנכי ה' אלהיך וגו'...., והוא אומרו מבית עבדים פירוש מקום שהוא של עבדים של ה' פירוש שממשלתו ממשלת שר אחד מעבדי ה' ולא רצה ה' שיהיו ישראל תחת ממשלת השרים אלא תחת ממשלתו יתברך בכל והוציאם מארץ מצרים לצד שהיא בית עבדים לתת להם ארץ אשר היא בית אלהים:

Or HaChaim on Exodus 20:2

(1) אנכי ה׳ אלוקיך, "I am the Lord your G'd, etc." The Zohar volume 1 page 108 comments on this that G'd handed out certain places on earth to the guardian angels of the various nations, and that the only land He did not assign to such guardian angels was the land of Canaan. G'd had reserved the land of Canaan for Himself. The Torah says מבית עבדים, describing the place as one assigned to one of G'd's servants (the guardian angel of Egypt). G'd did not want for the Jewish people to live in a homeland which "belonged" to the guardian angel of the Egyptians. He wanted the Israelites to reside in a country which was directly under His personal guidance.