The first verse of Shir HaShirim calls the Book LiSh’lomo, “Solomon’s”. Without going into the historical question of the authorship of the Book, the Midrash reads Shlomo as a reference to God, Mi shehashalom shelo – “The One to whom peace belongs”.
Shalom – here and elsewhere in Hebrew usage – is more than the absence of conflict. It is from a root that means completeness or perfection. God is the One who is complete and perfect, and He creates and engages the people of Israel to bring about perfection upon earth.
The connection with Shir HaShirim? If human beings earnestly, zealously, lovingly, work on bringing about a climate in which there are no jagged edges or deficiencies, the world will (in the words of the prayers) be “established as the Kingdom of the Almighty”.