NOTE: the Book of Wisdom must not be confused with Sirach, by Ben Sira, also known as Wisdom of Jesus son of Sirach, Wisdom of Ben Sira, (or Sirach) or Ecclesiasticus, a work from the second century BC, originally written in Hebrew.
According to St. Melito in the second century AD, it was considered canonical by Jews and Christians, and a Hebrew translation of the Wisdom of Solomon is mentioned by Naḥmanides in the preface to his commentary on the Pentateuch.
Date and authorship
The book is believed to have been written in Greek, but in a style patterned on that of Hebrew verse.  Although the author's name is nowhere given in the text, the writer was traditionally believed to be King Solomon because of references such as that found in IX:7-8, "Thou hast chosen me to be a king of thy people, and a judge of thy sons and daughters: Thou hast commanded me to build a temple upon thy holy mount..." The formulation here is similar to that of Ecclesiastes I:12, "I, Koheleth, was king in Jerusalem over Israel," which also fails to denote Solomon by name, but leaves no doubt as to whom the reader should identify as the author. However, the traditional attribution of The Book of Wisdom to Solomon has been soundly rejected in modern times. Says the Catholic Encyclopedia: "at the present day, it is freely admitted that Solomon is not the writer of the Book of Wisdom, which has been ascribed to him because its author, through a literary fiction, speaks as if he were the Son of David." Although the book of Wisdom is also called the Wisdom of Solomon, it was most likely composed centuries after the death of King Solomon. 
Scholars believe that the book represents the most classical Greek language found in the Septuagint, having been written during the Jewish Hellenistic period (the 1st or 2nd century BC). The author of the text appears well versed in the popular philosophical, religious, and ethical writings adopted by Hellenistic Alexandria.
Although purported to have the same author as Ecclesiastes, the beliefs on afterlife are significantly different. Chapter II in particular seems to be in direct response to the futilism of Ecclesiastes: "For they (the ungodly, in KJV) said within themselves, reasoning not aright, Short and sorrowful is our life; And there is no remedy when a man cometh to his end" (Wis. 2:1). Compare this, for example, with Ecclesiastes VI:12, "For who knoweth what is good for man in this life, all the days of his vain life which he spendeth as a shadow? for who can tell a man what shall be after him under the sun." It is clear that if not a direct response to the text of Ecclesiastes, the Book of Wisdom is at least taking issue with the philosophy of uncertainty and despair that Koheleth appears to preach.
In its place, Book of Wisdom offers the much more traditional and pious philosophy that trust and fear of God provide the path to redemption, e.g., (Wis. V:15) "But the righteous live for evermore; their reward also is with the Lord, and the care of them is with the most High." This is not the only such rejection of Koheleth's philosophy to be found in the Apocrypha. Ben Sira offers a direct rebuttal to the intellectualism of Koheleth's quest to "seek and search out by wisdom concerning all things that are done under heaven" (Ecc. I:13). Ben Sira writes "Seek not out the things that are too hard for thee, neither search the things that are above thy strength. But what is commanded thee, think upon with reverence; for it is not needful for thee to see with thine eyes the things that are in secret. Be not curious in unnecessary matters: for more things are shewed unto thee than men understand" (Ben Sirah 3:21-23).
The philosophical influences on the Book of Wisdom may include those of classical and Middle-Platonism. Some religious and ethical influences may stem from Stoicism, also found in the writings of the Alexandrian Jew, Philo, to whom Book of Wisdom has on occasion been wrongly attributed. (This is evident in the use of the four Stoic ideals which are borrowed from Plato.) A sorites appears in Chapter 6 (v. 17-20). This logical form is also called chain-inference, "of which the Stoics were very fond." (Zeller, Stoics, p. 216 note)
One passage (Wis. 8:2-18) has notable similarity to Virtue's speech to Heracles in Xenophon's Memorabilia, Book 2, 1:37.
Relation to other Jewish writings
Although the Book of Wisdom is non-canonical in the Rabbinical Jewish tradition, the work was at least known to medieval Jews, as Rabbi Moses ben Nachman (Ramban) attests. That it was known to ancient Jews as well is trivially true, as that was the milieu of its composition.
According to the Jewish Encyclopedia, the last section (9:18-19:22) is devoid of all connection with what precedes it. The speaker is no longer Solomon, but the author or the saints (16:28, 18:6 et passim), who recite the history of Israel's redemption from Egypt and other enemies. In like manner, the words are not addressed to the kings of the earth (9:18; 10:20; 11:4, 9, 17, 21; et passim), but to God, the deliverer from the Red Sea. The whole appears on close observation to be part of a Passover Haggadah recited in Egypt with reference to Gentile surroundings, and it accordingly abounds in genuine haggadic passages of an ancient character.
It is of some interest that the philosophy which the Book of Wisdom in Chapter II puts in the mouths of the "ungodly," presumably the Epicureans, bears strong literary resemblance to a prominent passage from the Jewish High Holiday liturgy, "Man begins from dust and ends in dust" (אדם יסודו מעפר וסופו לעפר) from the Unetanneh Tokef prayer (cf. Genesis 3:19: כי עפר אתה ואל עפר תשוב). The relevant verses from Book of Wisdom (II:2-5) read in part, "the breath in our nostrils is as smoke... our body shall be turned to ashes, and our spirit shall vanish as the soft air... our life shall pass away as the trace of a cloud... and shall be dispersed as a mist... for our time is a very shadow that passeth away." The Unetanneh Tokef prayer seems to offer a close parallel: "As to man, his origin is dust and his end is dust... he is like a broken vessel of clay, like withering grass, a fading flower, a passing shadow, a drifting cloud, a fleeting breath, scattering dust, a transient dream."
If this similarity is more than coincidence or the common citation of a third text, such as Isaiah 40:7, it would not be the only instance of Apocryphal influences on the Jewish liturgy. Elements of Ben Sira are also found in the High Holiday service and other prayers.
Messianic interpretation by Christians
Personification of Wisdom
There are found in the Book of Wisdom and other books of the wisdom literature to Wisdom as a personification with divine attributes. These have long been taken by Christian exegetes as references to Christ, who is called the wisdom of God by Paul the Apostle.
In chapter seven, Wisdom is said to be “the fashioner of all things” (v. 22). Because she fashions all things, is “an associate in his [God’s] works” (8:4), and is a “pure emanation of the glory of the Almighty” (7:25), Wisdom is eternal and one in being with the Father. Because Wisdom is God’s “creative agent”, she must be intimately identified with God himself. For Christians, the most definite indication that personified Wisdom refers to the Messiah is the paraphrasing of Wis 7:26 in Heb 1:3a. Wis 7:26 says that “she is a reflection of eternal light, a spotless mirror of the working of God, and an image of his goodness.” The author of Hebrews says of Christ: “He reflects the glory of God and bears the very stamp of his nature, upholding the universe by his word of power.”
Furthermore, Wisdom speaks of personified Wisdom in a Trinitarian way at 9:17: “Who has learned your counsel, unless you have given wisdom and sent your holy spirit from on high?”. The next verse says that salvation is an act of Wisdom. In Christianity salvation is an activity reserved for God, but it is here given to Wisdom, thus identifying them with one another.
The second chapter of the Book of Wisdom (Wisdom 2) builds up to a prophecy of Christ’s passion. First the ungodly men are described (Wis 1:16-2:9), followed by their plotting against the righteous man (2:10-20). The passage describes in detail the treatment of Jesus by the Jewish authorities. The first indication for Christians that it is a prophecy of the Messiah is in verse 11. Where the RSV reads weak, the Greek has achrestos, a play on the title Christos. Verse 12 is a quote of the LXX version of Is 3:10; Is 3:10 has been taken to refer to Jesus since the first-century Epistle of Barnabas. On the whole, this treatment of the suffering of the righteous man is heavily indebted to Isaiah; particularly the fourth Suffering Servant song (Is 52:13-53:12). Verse 13 uses pais (child, or servant), from Is 52:13. Verse 15 says his very sight is a burden, referencing Is 53:2. In verse 16 he calls God his father, which is thought to be based on a poor understanding of pais as in Is 52:13. Verse 18 is comparable to Is 42:1. Verse 19 makes reference to Is 53:7. A final reference to the Messiah is the righteous man’s “shameful death” in verse 20. This death has been identified with Jesus’ death on a cross, a cursed death hanging on a tree.
The Gospel of Matthew contains allusions to the Wisdom of Solomon. Parallels between Wisdom and Matthew include the theme of testing, and the mocking of a servant of God's claim to be protected by God. Matthew's gospel teaches that Jesus is the suffering servant of God. Wis 2:17-18 (Let us see if his words are true, and let us test what will happen at the end of his life; for if the righteous man is God’s son, he will help him, and will deliver him from the hand of his adversaries.) lent itself to Mt 27:43 (He trusts in God; let God deliver him now, if he desires him; for he said, ‘I am the Son of God.’”).