Our practice this year has been to read the Psalms, which contain 5 books, book by book. Now we return to Book V (Psalms 107-150) . The first series of psalms 111-118 are the “Hallelujah Psalms”. The “Egyptian Hallel (ps 113-118) was sung for the three great pilgrimage festivals, Passover, Weeks, and Tabernacles. The “Psalms of Ascent” (ps 120-134)  were used by pilgrims to or from Jerusalem. Psalm 136 is the “Great Hallel” for Sabbath services. Psalm 146-150 end the book with “Praise the Lord”.  Psalms 107 and 119 may be introductory psalms. 107 introduces the fifth book and 119 introduces the psalms of ascent.  Psalm 137 is untitled and unclassified. There are psalms of David in this book, 108-110 and 138-145.

You will find an introduction to the Psalms, here.

Here is a prayer from Gregory of Nazianus (329-389) who was an early Church father.

Lord, as I read the psalms let me hear you singing. As I read your words, let me hear you speaking. As I reflect on each page, let me see your image. And as I seek to put your precepts into practice, let my heart be filled with joy. Amen.
Psalm 113: A hymnThis is the beginning of the “Egyptian Hallel”, which are psalms sung at major Jewish festivals. Some scholars believe Psalms 113-114 were sung before the Passover meal and Psalms 115-118 were sung after the meal.  This psalm is also the last of the Hallelujah psalms (111-113). The phrase, “the name of the Lord” is a way of speaking about God.
Psalm 114:  A hymn like psalm.   This psalm recalls and celebrates the Exodus and the conquest of the land by naming the crossing of the sea and the river Jordan. Verse 8 refers to Ex 17.6; Num 20:11 when God provides water from a rock in the wilderness. Notice the parallelism and internal repetition in this psalm.
Psalm 115: A community petition.  This psalm asks God to show God’s glory to the nations. Israel’s God is contrasted to the other gods in verses 3-8. Then there is a call to trust (v 9-11), a blessing (v12-15).  Notice that ones called to trust are the same ones a blessing is asked upon. The psalm ends with thanksgiving. In the ancient world, the dead went to Sheol, the underworld which was a quiet place, not a place of praise.
Psalm 116: A psalm of Thanksgiving from an individual.  Verses 1-2 are a confession of faith that God will hear. Verses 3-4 the expression of need. Verses 5-11 are praise and thanksgiving. Verses 12-19 describe the fulfillment of vows in the Temple.
Psalm 117: A Hymn of praise. This is the shortest psalm. The psalm calls all nations to give thanks to God for the way God has treated “us”. Some scholars believe the “us” refers to Israel. What does it mean to call all nations to thank God for the way God has kept covenant with Israel?

Here are several good sources to aid your reading of the Psalms

Anderson, Bernhard W., Katheryn Pfister Darr, Understanding the Old Testament Abridged fourth Edition. (Upper Saddle River,New Jersey: Prentice Hall) 1998.

Clifford, Richard, “Psalms” in The New Oxford Annotated Bible with Apocrypha: New Revised Standard Version.Coogan, Michael D.; Brettler, Marc Z.; Perkins, Pheme; Newsom, Carol A. (2010-01-20) Oxford University Press. Kindle Edition.

Stuhlmueller, Carroll, “Psalms” in  HarperCollins Bible Commentary Mays, James L. ed.(San Francisco: HarperSanFrancisco) 2000.

McCann,Jr, J. Clifton “Psalms”,in The New Interpreter’s Bible Vol 3, Keck, Leander E. ed. (Nashville: Abingdon Press) 1996.