Blessed are you
YHVH our elo’ah
cosmic majesty
who remembers the [Noaḥide] covenant,
is faithful to the covenant,
and keeps their word.

Genesis 9:8-17
 
^9:8 Elohim said to Noaḥ and to his sons with him, saying: ⁹ “As for me – here, I am about to establish my covenant with you and with your seed after you, ¹⁰ and with all living beings that are with you: birds, herd-animals, and all the wildlife of the earth with you; all those going out of the Ark, of all the living-things of the earth. ¹¹ I will establish my covenant with you: All flesh shall never be cut off again by waters of the Deluge, never again shall there be Deluge, to bring the earth to ruin!” ¹² And Elohim said: “This is the sign of the covenant which I set between me and you and all living beings that are with you, for ageless generations: ¹³ My rainbow I set in the clouds, so that it may serve as a sign of the covenant between me and the earth. ¹⁴ It shall be: when I becloud the earth with clouds and in the clouds the rainbow is seen, ¹⁵ I will call to mind my covenant that is between me and you and all living beings – all flesh: never again shall the waters become a Deluge, to bring all flesh to ruin! ¹⁶ When the rainbow is in the clouds, I will look at it, to call to mind the age-old covenant between Elohim and all living beings – all flesh that is upon the earth.” ¹⁷ Elohim said to Noaḥ: “This is the sign of the covenant that I have established between me and all flesh that is upon the earth.”

Ezekiel 1:28
 
Like the appearance of the rainbow
that shines in the clouds on a day of rain,
such was the appearance of the surrounding radiance.
That was the appearance of the semblance of YHVH’s kavod.
When I beheld it, I flung myself down on my face.
And I heard the voice of someone speaking.

Bereshit Rabbah 35:3
 
“I set my rainbow (qashti)” —
[i.e.,] my Likeness (qishuti),
something which is likened (muqash) to Me.
Is this possible?
Rather, it resembles (qashin) [the Divine] as straw resembles grain.

Chagigah 16a:14
 
R. Judah, son of R. Nahmani, the interpreter of R. Simeon ben Lakish, expounded in a discourse:
When a person gazes at any one of three things, their eyes become dim:
at the rainbow, at the patriarch,^[1] A position of communal leader under Roman or other rule. For example, as held by Rabbi Yehuda haNasi in the 2nd-3rd cent. CE. , and at the cohanim.^[2] while offering the priestly blessing 
At the rainbow, as it is written,
“As the appearance of the rainbow in the cloud on a rainy day…
[so was] the appearance of the likeness of YHVH’s kavod.” (Ezekiel 1:28)

Chagigah 16a:11
 
[It is taught in the mishnah:]
Whoever has no concern for the honor of their Maker
deserves to have never come to the world. (Mishnah Chagigah 2:1)
[The Gemara asks:] Who is this [unconcerned with the honor of their Maker]?
Rabbi Abba said: “This is one who gazes at a rainbow.”
Rav Yosef said: “This is one who commits a transgression in private.”
Looking at a rainbow [is likened to a transgression of intimacy], as it is written:
“As the appearance of the rainbow that is in the cloud in the day of rain
so was the appearance of the brightness round about.
This was the appearance of the likeness of YHVH’s kavod” (Ezekiel 1:28)

Bereshit Rabbah 35:3
 
Another expounded: It is written:
“The rainbow shall be in the cloud, and I will see it,
to remember the eternal covenant
between Elohim and every living creature…” (Genesis 9:16) –
“between Elohim” – this is the attribute of justice above;
“and every living creature” – this is the attribute of justice below.
The attribute of justice above is severe;
the attribute of justice below is lenient.

Bereshit Rabbah 35:3
 
One of them expounded:
One verse says: “All objects cannot equal it” (Proverbs 8:11),
and one verse says: “All of your objects cannot equal it” (Proverbs 3:15).
“[All] objects” – these are mitsvot and good deeds.^[3] i.e., bringing kindness and justice to the world. I believe the midrashic parable here is suggesting that the Rainbow, as a symbol of divine justice (severe above and lenient below), is a memento to perform acts that are kind and just in positive fulfillment of the Noaḥide covenant. For a list of transgressions of this covenant, find the 7 Noaḥide laws. 
“Your objects” – these are precious stones and pearls.
Rabbi Aḥa in the name of Rabbi Tanḥum bar Rabbi Ḥiyya:
[Hashem said:] ‘My objects and your objects cannot equal it;
“Rather, let the one who praises, praise this:
perceiving and knowing Me,
for I am YHVH who performs kindness, justice…”’ (Jeremiah 9:23).

Artevan^[4] Probably a reference to Artabanus Ⅳ of Parthia, the last ruler of the Parthian Empire from c. 213 to 224.  sent a priceless jewel^[5] In gk., ἀτίμητος. Perhaps a pearl, although in the context of the rainbow, I imagine this to be a precious opal.  to our Rabbi.^[6] Rabbi Yehuda haNasi 
[Artevan] said to him: ‘Send me a valuable object that is as valuable as this.’
[Our Rabbi] sent him a mezuzah.
[Artevan] sent a message to him, saying:
‘I sent you an item that is priceless
and you sent me an item that is worth one polar.’
[Our Rabbi] said to [Artevan]: ‘My objects and your objects cannot equal it.
Moreover, you sent me an item that I must guard,
and I sent you an item that guards you while you sleep,
as it is stated: “It will guide you when you walk” (Proverbs 6:22) –
in this world.
“When you lie down, it will protect you” (Proverbs 6:22) –
at the moment of death.
“And when you awaken, it will be your conversation” (Proverbs 6:22) –
in the future.^[7] at the time of the resurrection of the dead ’

Pirkei Avot 5:6
 
Ten things were created on the eve of the Sabbath at twilight, and these are they:
[1] the mouth of the earth,^[8] the sinkhole that consumed Qoraḥ, Datan, Aviram and their followers 
[2] the mouth of the well,^[9] per midrash, the well of Miriam that irrigated the Camp of the Israelites 
[3] the mouth of the donkey,^[10] the abused jenny of the prophet Bilaam, who was gifted the ability to speak and advocate for herself given the dangerous circumstances that only she could perceive, and which Bilaam could not. 
[4] the rainbow [at the Noaḥide covenant]…

Berakhot 59a.12
 
And Rabbi Alexandri said that Rabbi Yehoshua ben Levi said:
One who sees a rainbow in a cloud must fall upon his face,
as it is stated: “As the appearance of the rainbow that is in the cloud…
And when I saw it, I fell upon my face” (Ezekiel 1:28).
In the West, [i.e., Erets Yisrael,] they would curse [this practice]
because it appears as one who is prostrating to the rainbow.
[As far as] blessing [is concerned,] however, [all agree that] one certainly recites a blessing.
What blessing [should one recite]?
Blessed… Who remembers the [Noaḥide] covenant.
It was taught in a baraita
that Rabbi Yishmael, son of Rabbi Yoḥanan ben Beroka, says:
[Blessed…] Who is faithful to their covenant
and fulfills their word.
Rav Pappa said: Therefore we will say them both [combined]:
Blessed… Who remembers the [Noaḥide] covenant
and is faithful to their covenant
and fulfills their word.