From a Judaeo-Christian perspective, to worship God is to praise Him. While it is true that, on the basis of number-count, laments (complains and cries to God for help) outnumber praises, the point of the laments is to move God to act to resolve what bring Him no glory so that praise and glory may once again rebound to Him. Furthermore, as we move through the Psalter, we are drawn into the vortex of praise in the 'halleluyah psalms' that conclude the Psalter (Psm 107-150). So dominant is this trend that the Hebrew name for the Psalter is Tehellim, 'Praises.'
People praise God for different reasons and their praises take different forms. Biblical scholars (thanks especially to the work of Claus Westermann) differentiate two broad categories (forms) of praise: Declarative Praise and Descriptive Praise.
Declarative Praise (or Thanksgiving Psalm) praises God in general terms, extolling His greatness and glory without detailing the background and specific reasons for praising Him. Yahweh is simply to be praised for who He is. All the 'hallelujah psalms' belong to this category. Examples of this category also include Psm
Descriptive Praise (or Hymn), on the other hand, praises God for specific acts of mercy. A narrative—the background that led to praise—is often part of the psalm. Examples of these are Psm
Arnold Anderson, "Psalm Study between 1955 and 1969," The Baptist Quarterly 23.4 (Oct 1969):155-163. This article, though dated, provides you with a quick and useful sketch of some of the most important works done in those years noted.
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