The "Song of songs," i. e., the best or most excellent of songs.
Which is Solomon's - literally, "to" or "for Solomon," i. e., belonging to Solomon as its author or concerning him as its subject. In a title or inscription, the former interpretation is to be preferred.

The song of songs - A song of peculiar excellence. See the Introduction. The rabbins consider this superior to all songs. Ten songs, says the Tarpon, have been sung; but this excels them all.
1. The first was sung by Adam when his sin was pardoned.
2. The second was sung by Moses and the Israelites at the Red Sea.
3. The third was sung by the Israelites when they drank of the rock in the wilderness.
4. The fourth was sung by Moses when summoned to depart from this world.
5. The fifth was sung by Joshua when the sun and moon stood still.
6. The sixth was sung by Deborah and Barak after the defeat of Sisera.
7. The seventh was sung by Hannah when the Lord promised her a son.
8. The eighth was sung by David for all the mercies given him by God.
9. The ninth is the present, sung in the spirit of prophecy by Solomon.
10. The tenth is that which shall be sung by the children of Israel when restored from their captivities. See the Targum.

The Song of songs, which is Solomon's. Wrote by Solomon, king of Israel, as the "amanuensis" of the Holy Ghost; and not by Hezekiah and his men, as the Jews say (k): or, "concerning Solomon" (l); Christ, of whom Solomon was a type; see Song 3:7; of his person, excellencies, love to his church, care of her, and concern for her; and of the nearness and communion he admitted her to, and indulged her with the Jews have a saying (m), that wherever the word Solomon is used in this song, the Holy One is meant, the holy God, or Messiah: it is called "the Song of songs", because the most excellent, as the Holy of holies, King of kings, &c. which, with the Hebrews, express a superlative; this being more excellent than the one hundred and five songs, written by Solomon, or than any human composure whatever; yea, preferable to all Scriptural songs, as to subject, manner of style, and copiousness of it.
(k) T. Bab. Bava Bathra, fol. 15. 1. (l) "de Solomone", Cocceius. (m) Maimon. Yesode Hatorah, c. 6. s. 12.

This is "the Song of songs," excellent above any others, for it is wholly taken up with describing the excellences of Christ, and the love between him and his redeemed people.

(CANTICLE I)--THE BRIDE SEARCHING FOR AND FINDING THE KING. (Son. 1:2-2:7)
The song of songs--The most excellent of all songs, Hebrew idiom (Exodus 29:37; Deuteronomy 10:14). A foretaste on earth of the "new song" to be sung in glory (Revelation 5:9; Revelation 14:3; Revelation 15:2-4).
Solomon's--"King of Israel," or "Jerusalem," is not added, as in the opening of Proverbs and Ecclesiastes, not because Solomon had not yet ascended the throne [MOODY STUART], but because his personality is hid under that of Christ, the true Solomon (equivalent to Prince of Peace). The earthly Solomon is not introduced, which would break the consistency of the allegory. Though the bride bears the chief part, the Song throughout is not hers, but that of her "Solomon." He animates her. He and she, the Head and the members, form but one Christ [ADELAIDE NEWTON]. Aaron prefigured Him as priest; Moses, as prophet; David, as a suffering king; Solomon, as the triumphant prince of peace. The camp in the wilderness represents the Church in the world; the peaceful reign of Solomon, after all enemies had been subdued, represents the Church in heaven, of which joy the Song gives a foretaste.

The title of the book at once denotes that it is a connected whole, and is the work of one author. - Song 1:1. The Song of Songs, composed by Solomon. The genitival connection, "Song of Songs," cannot here signify the Song consisting of a number of songs, any more than calling the Bible "The Book of books" leads us to think of the 24 + 27 canonical books of which it consists. Nor can it mean "one of Solomon's songs;" the title, as it here stands, would then be the paraphrase of שׁיר שׁירי שׁ, chosen for the purpose of avoiding the redoubled genitives; but "one of the songs" must rather have been expressed by שׁיר משּׁירי. It has already been rightly explained in the Midrash:
(Note: Vid., Frst's Der Kanon des A. T. (1868), p. 86.)
"the most praiseworthy, most excellent, most highly-treasured among the songs." The connection is superl. according to the sense (cf. ἄῤῥητα ἀῤῥήτων of Sophocles), and signifies that song which, as such, surpasses the songs one and all of them; as "servant of servants," Genesis 9:25, denotes a servant who is such more than all servants together. The plur. of the second word is for this superl. sense indispensable (vid., Dietrich's Abhand. zur hebr. Gramm. p. 12), but the article is not necessary: it is regularly wanting where the complex idea takes the place of the predicate, Genesis 9:25; Exodus 29:37, or of the inner member of a genitival connection of words, Jeremiah 3:19; but it is also wanting in other places, as Ezekiel 16:7 and Ecclesiastes 1:2; Ecclesiastes 12:8, where the indeterminate plur. denotes not totality, but an unlimited number; here it was necessary, because a definite Song - that, namely, lying before us - must be designated as the paragon of songs. The relative clause, "asher lishlōmō," does not refer to the single word "Songs" (Gr. Venet. τῶν τοῦ), as it would if the expression were שׁיר מהשּׁ, but to the whole idea of "the Song of Songs." A relative clause of similar formation and reference occurs at 1-Kings 4:2 : "These are the princes, asher lo, which belonged to him (Solomon)." They who deny the Solomonic authorship usually explain: The Song of Songs which concerns or refers to Solomon, and point in favour of this interpretation to lxx B. ὃ ἐστι Σαλ., which, however, is only a latent genit., for which lxx A. τῷ Σαλ. Lamed may indeed introduce the reference of a writing, as at Jeremiah 23:9; but if the writing is more closely designated as a "Song," "Psalm," and the like, then Lamed with the name of a person foll. is always the Lamed auctoris; in this case the idea of reference to, as e.g., at Isaiah 1:1, cf. 1-Kings 5:13, is unequivocally expressed by על. We shall find that the dramatized history which we have here, or as we might also say, the fable of the melodrama and its dress, altogether correspond with the traits of character, the favourite turns, the sphere of vision, and the otherwise well-known style of authorship peculiar to Solomon. We may even suppose that the superscription was written by the author, and thus by Solomon himself. For in the superscription of the Proverbs he is surnamed "son of David, king of Israel," and similarly in Ecclesiastes. But he who entitles him merely "Solomon" is most probably himself. On the other hand, that the title is by the author himself, is not favoured by the fact that instead of the שׁ, everywhere else used in the book, the fuller form asher is employed. There is the same reason for this as for the fact that Jeremiah in his prophecies always uses asher, but in the Lamentations interchanges שׁ with asher. This original demonstrative שׁ is old-Canaanitish, as the Phoenician אש, arrested half-way toward the form asher, shows.
(Note: From this it is supposed that asher is a pronom. root-cluster equivalent to אשׁל. Fleischer, on the contrary, sees in asher an original substantive athar = (Arab.) ithr, Assyr. asar, track, place, as when the vulgar expression is used, "The man where (wo instead of welcher) has said.")
In the Book of Kings it appears as a North Palest. provincialism, to the prose of the pre-exilian literature it is otherwise foreign;
(Note: We do not take into view here Genesis 6:3. If בּשׁגם is then to be read, then there is in it the pronominal שׁ, as in the old proper name Mishael (who is what God is?).)
but the pre-exilian shir and kinah (cf. also Job 19:29) make use of it as an ornament. In the post-exilian literature it occurs in poetry (Psalm 122:3, etc.) and in prose (1-Chronicles 5:20; 1-Chronicles 27:27); in Ecclesiastes it is already a component part of the rabbinism in full growth. In a pre-exilian book-title שׁ in place of asher is thus not to be expected. On the other hand, in the Song itself it is no sign of a post-exilian composition, as Grtz supposes. The history of the language and literature refutes this.

The song - The most excellent of all songs. And so this might well be called, whether you consider the author of it, who was a great prince, and the wisest of all mortal men; or the subject of it, which is not Solomon, but a greater than Solomon, even Christ, and his marriage with the church; or the matter of it, which is most lofty, containing in it the noblest of all the mysteries contained either in the Old or the New Testament; most pious and pathetical, breathing forth the hottest flames of love between Christ and his people, most sweet and comfortable, and useful to all that read it with serious and Christian eyes.