James Kinsley, ed., Poems and Songs of Robert Burns, 3 vols (Oxford: Clarendon Press, 1968): index of titles and first lines at end of vol.II; commentary in vol. III: PR4300 1968 .O9
G. Ross Roy, ed., Letters of Robert Burns, 2 vols., 2nd ed. (Oxford: Clarendon Press, 1985): PR4331 .A4 1985
James C. Dick, ed., The Songs of Robert Burns (orig. 1903; repr. Hatfield PA: Folklore Assoc., 1962): M1746.B94 S7
Nigel Leask, ed., The Oxford Edition of the Works of Robert Burns: Commonplace books, Tour Journals and Miscellaneous Prose, vol. 1 (Oxford: Oxford University Press, 2014).
J. W. Egerer, A Bibliography of Robert Burns (Edinburgh: Oliver & Boyd, 1964; Carbondale: Southern Illinois UP, 1965): PR4328 .E43 1965
Catalogue of Robert Burns Collection, the Mitchell Library, Glasgow (Glasgow: Glasgow City Libraries, 1996): PR 4328 .M5 1996
Elizabeth Sudduth, The G. Ross Roy Collection of Robert Burns, an illustrated Catalogue (Columbia, SC: Univ. of South Carolina Press, 2009): PR4331 .S8 2009 (note that subsequent additions to the Roy Collection are available in the main online library catalogue).
Memorial Catalogue of the Burns Exhibition: held in the Galleries of the Royal Glasgow Institute (Glasgow: Hodge, 1898): PR4335 .B86 1898
Larissa P. Watkins, Burnsiana: a Bibliography of the William R. Smith Collection in the Library of the Supreme Council, 33rd degree, SJ (Newcastle, DE: Oak Knoll, 2008): PR4328 .W37 2008
For a full list, including many first periodical and chapbook appearances, see the bibliography of Burns by J. W. Egerer (in the Bibliographies panel).
Poems, Chiefly in the Scottish Dialect (Kilmarnock: John Wilson, 1786); PR4300 1786 .K1
Poems, Chiefly in the Scottish Dialect (Edinburgh: Creech, 1787); PR 4300 1787 .E3 (There are two type-settings of the first part of the book, with the second setting distinguished by having the misprint "stinking" for "skinking" in "Address to a Haggis."; Copy 1 in the Roy Collection belonged to Burns's friend Robert Ainslie and has annotations in Burns's handwriting)
Poems, Chiefly in the Scottish Dialect (London: Strahan, 1787): PR 4300 1787 .L6
[Also issued as: Poems, Chiefly in the Scottish Dialect (Dublin: William Gilbert, 1787): PR 4300 1787 .D8]
Poems, Chiefly in the Scottish Dialect (Philadelphia: Stewart and Hyde, 1788): PR4300 1788 .P3
Poems, Chiefly in the Scottish Dialect (New York: J. and A. M'Lean, 1788): PR 4300 1788 .N4
Poems, Chiefly in the Scottish Dialect, 2 vols (Edinburgh: Creech, 1793); PR 4300 1793 .E3 (Vol. II includes the first appearance of "Tam o' Shanter" in any of Burns's collections)
Poems, Chiefly in the Scottish Dialect, 2 vols (Edinburgh: Creech, 1794); PR 4300 1794 .E3
Many of Burns's poems were not published in any collection of his work during his lifetime, and for research on these the information (and misinformation) provided by his nineteenth-century editors remains important.
The words for the songs Burns wrote are usually included in collections of his poems (e.g. in the Kinsley edition), but not always with the music. For fuller information on available editions and recordings, see the separate page on Burns's Songs
The first collection of Burns's poems, published by subscription, July 31, 1786, and printed for Burns by John wilson of Kilmarnock in an edition of 612 copies. Available here from the University of Glasgow
Carol McGuirk, ed., Selected Poems, Penguin Classics (Harmondsworth: Penguin, 1993 etc.)
Robert Irvine, ed., Selected Poems and Songs (Oxford: Oxford UP, 2013)
Robert Crawford and Christopher Whateley, ed., The Best-laid Schemes: Selected Poetry and Prose (Princeton NJ: Princeton UP, 2009)
Andrew Noble and Patrick S. Hogg, ed., The Canongate Burns (Edinburgh: Canongate Classics, 2001, revd. 2003).
Robert Donald Thornton, ed., Selected Poetry and Prose, Riverside editions (Boston: Houghton Mifflin, 1966)
Not all the poems added to the Burns canon after his death were genuine.