Hashem causes the Sea of Reeds to split, rescuing the Children of Israel from the oncoming Egyptians. At this magnificent manifestation of Hashem’s Presence,
Then Moshe and the Children of Israel undertook to sing this song to Hashem. They said as follows:
I will sing to Hashem, for He is greatly exalted;
Horse and rider He cast down in the sea.
Hashem is my strength and my praise, and He has become my salvation; This is my G-d and I will house Him (V’ANVEHU);
the G-d of my father, and I will exalt Him. (Shemot 15:1-2).

The word V’ANVEHU presents a translation problem: It is clearly a verb, but what is its root? The Midrash (Mechilta Shira, Ch. 3) includes a number of opinions, many of which are adopted by the commentaries. One view relates V’ANVEHU to NOI, “beauty”; accordingly, says Rashi in his second translation, this means
“I will tell of His beauty and praise to the people of the world.”
Alternatively, says R. Yishmael in the Mechilta (loc. cit.),
“I will beautify myself with mitzvot: I will make a beautiful lulav, a beautiful sukkah, beautiful tzitzit, and beautiful tefillin.”

Our translation, however,
and I will house Him,
follows the view of R. Yosi ben-Dormaskit in the Mechilta, as well as Targum Onkelos (the translation of the Torah into Aramaic) and is Rashi’s first translation:
“And I will build Him a Sanctuary.”
from the word , home.

The anthology Yalkut Lekach Tov quotes R. Eliyahu Mishkovsky, who derives a fundamental principle in serving Hashem from this: When one experiences an uplifting of the spirit, one must strengthen that awakening with a commitment to concrete action. Otherwise, the inspiration might dissipate.

Still, we might ask, why this commitment? Why does
This is my G-d
necessarily lead to
V’ANVEHU - And I will build Him a Sanctuary -?

The Israelites experience unsurpassed, nationwide Divine revelation, as Rashi puts it:
“This is my G-d: In His Glory He was revealed to them and they pointed to Him. At the sea, a maidservant saw what [even] the prophets did not see.”
In response to this vision they commit themselves to building a Sanctuary to Hashem.

Malbim explains further that the purpose of the Sanctuary will be to understand Hashem’s constant connection to the universe:
“This is my G-d: He is my G-d Whom I have apprehended through the senses and recognized through the miracles He did for us. I saw with my eyes, like one who points out that this is He. Consequently, and I will house Him: He will reside in our midst – the Holy One in His holy abode – and His Presence will be within us until all shall know Him and perceive His Guidance and Providence.”
And Sforno adds that we maintain this connection with Hashem through our devotion:
“I will make an abode to cause Him to reside in our midst, and I will pray in it to Him alone, and I will worship appropriately to He who bestows good or bad, for the intent of service and prayer is to find favor.”

The theme of building the Sanctuary is further developed in the Song at the Sea:
You, in Your kindness, led the nation which You redeemed;
You, in Your strength, guided [them] to Your holy abode (NEVEI).
May You bring them and implant them on the mountain of Your inheritance; the foundation of Your dwelling which You have made, Hashem; the Sanctuary, my L-rd, that Your hands established (verse 13,17).
The desire to build a Sanctuary is most immediately fulfilled by constructing the Mishkan, described in fine detail in the latter part of the Book of Shemot (chapters 25-31, 35-40). This explains why the Book of Shemot includes the Mishkan and concludes with Hashem’s Glory filling the Mishkan.

The impetus to build a house dedicated to Hashem comes from man, in response to feeling Hashem’s closeness and protection:
. . . When He will give you rest from all your enemies all around, and you will dwell securely. It shall be that the place where Hashem, your G-d, shall choose to make His name reside there . . . (Devarim 12:10-11).
Our Sages teach (Sanhedrin 20b; Rambam, Hilchot Melachim 1:1,2), therefore, that the mitzvah to build a permanent sanctuary follows that of establishing a king and of eradicating Amalek.

David felt this impulse:
And it was, when the king dwelled in his house, and Hashem had given him rest all around from all his enemies, that the king said to Natan the prophet, “See now, I dwell in a house of cedar, but the ark of G-d dwells within the curtains” (Shmuel II 7:1-2).
Ultimately, Shlomo fulfills his father’s desire:
I have surely built a habitation for You, a foundation of Your dwelling forever (Melachim I 8:13).

But, the origin of this impetus derives from our Patriarch Yaakov:
And Yaakov awoke from his sleep and he said, “Indeed, there is Hashem in this place, but I did not know”. And he feared and said, “How awesome is this place! This is nothing but the house (BEIT) of G-d, and this is the gate of heaven.” And Yaakov arose early in the morning and he took the stone that he had placed at his head and set it up as a pillar and poured oil on its top. And he called the name of the place Beit-El . . . And Yaakov took an oath, saying . “. . . this stone which I have set up as a pillar shall be a house of G-d . . .” (Bereishit 28:16-20, 22)
Although Avraham thought of the place of encounter with Hashem as “mountain,” and Yitzchak called it “field,” Yaakov uniquely called it “house” (Pesachim 88a). Yaakov feels Hashem’s Presence and, rather than dedicate a part of nature to His service, desires to construct an abode, like his own home, where G-d and man can co-exist.

This becomes a model for his descendants, for when the Children of Israel say
This is my G-d V’ANVEHU - And I will build Him a Sanctuary
they are reiterating their Patriarch’s oath.