The author of this psalm, as of those which immediately precede it, is unknown. It is very general in its character, and has no allusion to any circumstances by which one could determine the name of the author, or the occasion on which it was written. In connection with the five following psalms, it constitutes what was known among the Hebrews as the "Hallel'; that is, the song of praise, sung on great occasions, at the annual festivals, and especially at the Passover and the Feast of tabernacles. Buxtorf, Lexicon. Tal., p. 613, et al.
This psalm, which is expressive of the majesty of God, as having a claim to universal praise, consists essentially of two parts:
I. The general statement that God is to be praised, and a call on all to engage in that service, Psalm 113:1-3.II. Reasons why he should be praised, Psalm 113:4-9.
(1) he is exalted above all nations, Psalm 113:4;
(2) None can be compared with him, Psalm 113:5;
(3) he is condescending, and looks with interest on the things in heaven and on earth, Psalm 113:6;
(4) He exalts the poor to positions of honor and influence, Psalm 113:7-8;
(5) He constitutes and appoints families, with all that is tender and joyous in the domestic relation, Psalm 113:9.

An exhortation to bless God for his own excellencies, Psalm 113:1-6; and for his great mercy to the poor and necessitous, Psalm 113:7-9.
Psalm 113:1-9, Psalm 114:1-8, 115, 116, Psalm 117:1-2, and 118, form the great Hallel, and were sung by the Jews on their most solemn festivals, and particularly at the passover. To these reference is made by the evangelists, Matthew 26:30, and Mark 14:26, there called the hymn which Jesus and his disciples sung at the passover, for the whole of the Psalm were considered as one grand hymn or thanksgiving. It was probably composed after the return from the captivity. It has no title but Hallelujah in the Hebrew and ancient Versions.

INTRODUCTION TO PSALM 113
With this psalm begins the great "Hallel", which ends with Psalm 118; and was used to be sung at the Jewish festivals, particularly at the feast of tabernacles and of the passover; and is thought by some to be the hymn sung by Christ and his apostles, after the celebration of the Lord's supper; in which there are many things pertinent to that occasion as well as to the above feasts. This psalm is a song of praise for redemption by Christ, to be sung in Gospel times, when the name of the Lord should be known among all nations, from the rising to the setting sun. It is thought by some to be an abridgment of the song of Hannah, 1-Samuel 2:1, there is an agreement.

An exhortation to praise God.

Hallelujah to Him Who Raiseth Out of Low Estate
With this Psalm begins the Hallel, which is recited at the three great feasts, at the feast of the Dedication (Chanucca) and at the new moons, and not on New Year's day and the day of Atonement, because a cheerful song of praise does not harmonize with the mournful solemnity of these days. And they are recited only in fragments during the last days of the Passover, for "my creatures, saith the Holy One, blessed be He, were drowned in the sea, and ought ye to break out into songs of rejoicing?" In the family celebration of the Passover night it is divided into two parts, the one half, Psalm 113:1-9, Psalm 114:1-8, being sung before the repast, before the emptying of the second festal cup, and the other half, Psalm 115:1, after the repast, after the filling of the fourth cup, to which the humnee'santes (Matthew 26:30; Mark 14:26) after the institution of the Lord's Supper, which was connected with the fourth festal cup, may refer. Paulus Burgensis styles Psalm 113:1 Alleluja Judaeorum magnum. This designation is also frequently found elsewhere. But according to the prevailing custom, Psalm 113:1, and more particularly Psalm 115:1, are called only Hallel, and Ps 136, with its "for His mercy endureth for ever" repeated twenty-six times, bears the name of "the Great Hallel" (הלּל הגּדול).
(Note: Vid., the tractate Sofrim, xviii. 2. Apart from the new moons, at which the recitation of the Hallel κατ ̓ ἐξοχήν, i.e., Psalm 113-118, is only according to custom (מנהג), not according to the law, the Hallel was recited eighteen times a year during the continuance of the Temple (and in Palestine even in the present day), viz., once at the Passover, once at Shabuoth, eight times at Succoth, eight times at Chanucca (the feast of the Dedication); and now in the Exile twenty-one times, because the Passover and Succoth have received two feast-days and Shabuoth one as an addition, viz., twice at the Passover, twice at Shabuoth, nine times at Succoth. Instead of Hallel absolutely we also find the appellation "the Egyptian Hallel" (הלּל המּצרי) for Psalm 113-118. The ancient ritual only makes a distinction between this (Egyptian) Hallel and the Great Hallel, Ps 136 (see there).)
A heaping up, without example elsewhere, of the so-called Chirek compaginis is peculiar to Psalm 113:1-9. Gesenius and others call the connecting vowels i and o (in proper names also u) the remains of old case terminations; with the former the Arabic genitive termination is compared, and with the latter the Arabic nominative termination. But in opposition to this it has been rightly observed, that this i and o are not attached to the dependent word (the genitive), but to the governing word. According to the more probable view of Ewald, 211, i and o are equivalent connecting vowels which mark the relation of the genitive case, and are to be explained from the original oneness of the Semitic and Indo-Germanic languages.
The i is found most frequently appended to the first member of the stat. constr., and both to the masc., viz., in Deuteronomy 33:16; Zac 11:17 (perhaps twice, vid., Khler in loc.), and to the femin., viz., in Genesis 31:39; Psalm 110:4; Isaiah 1:21. Leviticus 26:42; Psalm 116:1 hardly belong here. Then this i is also frequently found when the second member of the stat. constr. has a preposition, and this preposition is consequently in process of being resolved: Genesis 49:11; Exodus 15:6, Obadiah 1:3 (Jeremiah 49:16), Hosea 10:11; Lamentations 1:1; Psalm 123:1, and perhaps Song 1:9. Also in the Chethb, Jeremiah 22:23; Jeremiah 51:13; Ezekiel 27:3. Thirdly, where a word stands between the two notions that belong together according to the genitival relation, and the stat. construct. is consequently really resolved: Psalm 101:5; Isaiah 22:16; Micah 7:14. It is the same i which is found in a great many proper names, both Israelitish, e.g., Gamaliel (benefit of God), and Phoenician, e.g., Melchizedek, Hanniba‛al (the favour of Baal), and is also added to many Hebrew prepositions, like בּלתּי (where the i however can, according to the context, also be a pronominal suffix), זוּלתי (where i can likewise be a suffix), מנּי (poetical). In אפסי, on the other hand, the i is always a suffix. The tone of the i only retreats in accordance with rhythmical rule (vid., Psalm 110:4), otherwise i is always accented. Psalm 112:8 shows how our Psalm 113:1-9 in particular delights in this ancient i, where it is even affixed to the infinitive as an ornament, a thing which occurs nowhere else, so that להושׁיבי excites the suspicion of being written in error for להושׁיבו.
Among those things which make God worthy to be praised the Psalm gives prominence to the condescension of the infinitely exalted One towards the lowly one. It is the lowliness of God lowering itself fro the exaltation of the lowly which performs its utmost in the work of redemption. Thus it becomes explicable that Mary in her Magnificat breaks forth into the same strain with the song of Hannah (1 Sam. 2) and this Psalm.