Psalms 135, 136, 138, and 139 are Psalms of thanksgiving. Psalm 135 is a song of praise for God's wonderful works in nature and in history. A nation that is now cleansed and converted worships God in this Psalm. The call to worship is found in verses 1-4; adoration to Him who controls nature in verses 5-7; adoration to Him who redeemed the nation and set it in Palestine in verses 8-18; and adoration to Him who is above all gods and therefore worthy of all worship in verses 19-21.
Psalm 136 seems to be an extension of Psalm 135 and is continuing praise to Almighty God. Also, it is called a Hallel Psalm, which means it was sung at the opening of the Passover and was a favorite Temple song.
One of the great themes of the Bible is the mercy of God. In Psalm 136 alone the word "mercy" is found 26 times, one time for each verse. Perhaps it would be helpful for us to distinguish between mercy and grace. They are not one and the same. One is negative and one is positive. One keeps us from hell, and the other assures us of heaven. Mercy is not getting what you deserve (hell and judgment), while grace is getting that which you do not deserve (heaven and God's blessing).
In Psalm 137 the Jewish captives hung their harps on the trees beside a river near Babylon and sat down and wept. They had been captured by the enemy for their disobedience. But even in captivity they would trust that God's mercy would not forsake them. And they would not be let down.
