Of all the manuscripts discovered in the Judaean Desert, the Psalms are represented more than any other book; one or more Psalms are found in thirty-six scrolls from Qumran and three from other sites. The purpose of this study is twofold: to make available in one place much of the data contained in these manuscripts, and to investigate the main issues arising from study of this material. In PART I, the question of appropriate terminology is addressed, and four kinds of information are presented: a description of all the Psalms scrolls; a listing of variant readings by manuscript; the same variants listed by Psalm and verse; and a synopsis of superscriptions in the scrolls, the Masoretic Psalter and the Septuagint. Additional primary material is provided in the Appendices, including the contents of the Psalms scrolls by manuscript and by Psalm and verse. In PART II, six issues that arise from study of the Psalms scrolls are investigated with the following results: (a) These manuscripts attest to stabilization of the Psalter in two gradual stages. (b) At least two Psalters are found among the Dead Sea Scrolls (the MT-150 collection and the 11QPsa collection). (c) The structure of 11QPsa, by far the most extensive of the scrolls, may be explained in terms of Davidic emphasis, genre, and other principles. (d) The 11QPsa Psalter was compiled among circles who used the solar calendar, possibly the Qumran community itself. (e) 11QPsa qualifies as an edition of the Book of Psalms--not a secondary or derivative collection--on the basis of attribution to David, structural principles, and usage. (f) While the Vorlage of the Septuagint Psalter is not evident in any single Psalms manuscript, several shared variants and passages show that the translator's Hebrew text contained many readings found in specific scrolls but not in the Masoretic Text.