COMPLETE TITLE: The Analysis of Beauty. Written with a view of fixing the fluctuating Ideas of Taste. By William Hogarth.
Online text: Digital Library for the Decorative Arts and Material Culture 

LATER EDITIONS:
The Analysis of Beauty. Written with a view of fixing the fluctuating Ideas of Taste. By William Hogarth. A New Edition, London, Printed by J. Reeves for the author, 1772; London, printed by W. Strahan, for Mrs. Hogarth, and sold by her at her house in Leicester-Fields, 1772.
Online text: INTERNET ARCHIVE

The Analysis of Beauty, by William Hogarth. And, Rules for drawing Caricaturas: with An Essay on Comic Painting, by Francis Grose. With Plates, London, Samuel Bagster, [1791?].

The Analysis of Beauty. Written with a view of fixing the fluctuating Ideas of Taste. By William Hogarth. Illustrated by Engravings. A New Edition, Printed Verbatim from the Original Work, the Pages of which are here Retained, London, Printed for R. Scholey by T. Davison, 1810.
Online text: GOOGLE BOOKS

The Analysis of Beauty. Written with a view of fixing the fluctuating Ideas of Taste. By William Hogarth, Edinburgh, Printed by James Ballantyne & Co., 1810.

The Analysis of Beauty. Written with a view of fixing the fluctuating Ideas of Taste. By William Hogarth, [London], Samuel Bagster, 1822.

The text was included in various edition of the complete works of Hogarth:
- Anecdotes of Mr. Hogarth, and Explanatory Descriptions of the Plates of Hogarth Restored, London, Printed for the engraver [Thomas Cook] and G. and J. Robinson, 1803.
- The Works of William Hogarth, (Including the 'Analysis of Beauty',) Elucidated by Descriptions, Critical, Moral and Historical; (Founded on the Most Approved Authorities.) To which is Prefixed Some Account of His Life. By Thomas Clerk. In Two Volumes, London, Printed for R. Scholey, 46, Paternoster-Row; by James Ballantyne & Co. Edinburgh, 1810, 1812, 1821, 2 vols.; London, Black and Armstrong, 1837, 3 vols.
Online text: 1812 edition 
- Anecdotes of the Celebrated William Hogarth; with an Explanatory Description of his Works. With a portrait, London, printed for John Stockdale, 1811 and 1813.
Online text: 1813 edition
- The Complete Works of William Hogarth, including the Analysis of Beauty, Printed Verbatim from the Author's own Edition: with Descriptions Critical, Moral, and Historical, and some Account of His Life, London, S. Cornish, 1838, 3 vols.

RECENT EDITIONS:
Reprints of the first edition:
- The Analysis of Beauty by William Hogarth. A Reprint Including the Plates Formerly in Portfolio, ed. by W.C. Ostrander, Pittsfield, Mass., The Silver Lotus Shop, 1909. Some parts of the original text are omitted (the Preface, replaced by a new preface by Ostrander, the Introduction, and various notes).
Online text: INTERNET ARCHIVE
- The Analysis of Beauty. With the rejected passages from the manuscript drafts and autobiographical notes. Edited with an introduction by Joseph Burke, Oxford, Clarendon Press, 1955.
- Menston, Scolar Press, 1971.
- New York, NY, Garland, 1973.
- Ilkley; London, Scolar Press, 1974.
- Hildesheim; New York, Georg Olms, 1974 and 2001.
- The Analysis of Beauty by William Hogarth. Edited with an introduction and notes by Ronald Paulson, New Haven; London, Published for the Paul Mellon Centre for British Art by Yale University Press, 1997.

TRANSLATIONS:
Italian: L'analisi della Bellezza. Scritta col disegno di fissar l'Idee vaghe del Gusto. Tradotta dall'Originale Inglese. Di Guglielmo Hogarth, Livorno, Giovanni Paolo Fantechi, 1761 (see). The translation is anonymous.
Also worth mentioning is: L'analisi della bellezza, translation by C. Maria Laudando; presentation by Laura Di Michele, Palermo, Aestethica, 1999.

French: Analyse de la Beauté, Destinee a fixer les Idées vagues qu'on a du gout; traduite de l'anglais de Guillaume Hogarth; Précédée de la vie de ce peintre, et suivie d'une Notice chronologique, historique et critique de tous ses ouvrages de peinture et de gravure, avec deux grandes planches, Paris, L'auteur, Levrault, Schoell et Compagnie, 1805, 2 vols. in 1 (see). Translation by Hendrik Jansen, Bibliothecaire de S. E. Mgr. de Talleyrand-Perigord (the name appears in the dedication to Monseigneur Charles Theodore, Electeur et Archeveque de Ratisbonne).
Also to be mentioned is a more recent translaton: William Hogarth. L'Analyse de la beauté. Introduction, traduction et notes par Olivier Brunet, Paris, A.G. Nizet, 1963.

German: Zergliederung der Schönheit, die schwankenden Begriffe von dem Geschmack festzusetzen, geschrieben von Wilhelm Hogarth. Aus dem Englischen übersetzt von C. Mylius, London, Andreas Linde, Hannover, J. W. Schmidt, 1754 (see). Translation by Christlob Mylius, in collaboration with Hogarth.
Also to be mentioned is a more recent translation: Analyse der Schönheit. Aus dem Englischen von Jörg Heininger. Mit einem Nachwort von Peter Bexte, Dresden, Verlag der Kunst, 1995; Hamburg, Philo Fine Arts, 2008.

Russian: Analiz krasoty, Leningrad; Moskva, 1958 (see).

Also worth mentioning is the Ukrainian translation: Kyïv, s.n., 1978.