“Let them make Me a sanctuary, that I may dwell in their midst.” [1] 
The Kotzker explained:
“…every man should build in his heart a sanctuary, so that G-d may dwell in it.” [2]

Philo wrote:

“. . . For the beginning and end of happiness is to be able to see G-d. But this cannot happen to him who has not made his soul . . . a sanctuary and altogether a shrine of God.” [3]

For the Talmud, “the heart” meant performing the mitzvoth in a spirit of donating our heart to G-d:

אין לו להקב״ה בעולמו אלא ד׳ אמות של הלכה בלבד
“[From the destruction of the Temple,] the Blessed Holy One has only the four cubits of Halachah in this world.” [4]

The Zohar discourses on the Jewish liturgy as its commentary on parshah Terumah — teaching that the Mishkan is built by donating our heart during the traditional prayers.

For all the outward details of the Mishkan, the deeper understanding of it is always as something that should happen in our heart. We are the Mishkan:

“Hashem lives within the soul of everyone who lets Him in…We cry over the destruction of [the Temple], yet we can be that structure who carries within the presence of Hashem.” [5]

and

“[Torah] says ‘Let them make me a Sanctuary that I may dwell בתוכם/among (or within) them’ — in them, the people, not in it, the sanctuary. We are each to build a Tabernacle in our own heart for G-d to dwell in.” [6]

Yet, isn’t G-d always Present everywhere?

“The heavens, even the highest heaven, cannot contain you. How much less this temple I have built!” [7]

How, then, can we let G-d into our hearts, if the Temple itself wasn’t sufficient to contain that Holiness?

Perhaps we could reconsider what is meant by “letting G-d in.”

Understand: G-d is already in your heart.

But G-d is unrevealed because of things that you, yourself, mistakenly put in the way:

“But your sins have separated you from your G-d; your sins have hidden His face from you..” [8]

“Sins” are not ultimate criteria for your worth or spiritual value. Those remain unchanged regardless of what you do. “Sins” are errors; mistakes. They are mistaken beliefs; mistaken things we do. “Mistaken beliefs” — a wrong belief that anything exists separate from G-d. In a more extreme statement, a wrong belief that anything exists except G-d. “Mistaken things we do” — things we do mistakenly believing that the consequences are escapable or non-existent. These mistakes obscure the holiness that is already here.

We correct these by replacing them.

We can correct mistaken belief by contemplating the Rambam’s statement on “Primary Being” and other such statements:

“There is no presence without His Presence; there is no life with out His Life; there is no substance without His Substance; there is no particle, no atom, without Him at its very core.” [9]

Doing so, we replace a mistaken belief in G-d’s distance with the accurate one of G-d’s intimate closeness.

We can correct mistaken things we do by t’shuvah — “returning” — and by realizing that G-d responds to all that we do “midah k’neged midah” — “measure for measure.”

Doing so, we replace “wrong” actions with “right ones,” although we can only be ultimately successful in this with G-d’s help.

“Replacing” mistakes is like cleaning a window. When we remove the dust, the sun shines in by itself.

In the same way, when we replace a mistaken belief or action, we do so best with an attitude of removing an obstruction to the revelation of G-d’s Presence in us.

Then — we are building a Mishkan in ourselves; letting G-d in.

See also:

https://rabbielimallon.wordpress.com/2012/02/25/2-25-12-terumah-the-meaning-of-a-mishkan/

https://rabbielimallon.wordpress.com/2011/02/07/2-7-11-in-my-heart-bilvavi/

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[1] Sh’mot/Ex. 25:8
[2] Newman, Hasidic Anthology; p. 8, #6
[3] Philo; Questions and Answers on Exodus, n. 51
[4] Berachot 8a
[5] http://www.neveh.org/friedman/parsha/vayakhail.html
[
6] Malbim; quoted in Plaut, G.; The Torah: A Modern Commentary; Union for Reform Judaism, © 2005; p. 557 (no further citation given)
[7] I Kings 8:27 (Shlomo Ha-Melech/King Solomon at the dedication of the First Temple)
[8] Yishiyahu/Isa. 59:2
[9] Lichtenstein, Rabbi Morris; Jewish Science and Health; Jewish Science Publishing Co., © 1925; p. 14