The publishing history of this edition, and its relationship to other translations of what is commonly known as "The Mabinogion," is a little complicated, and I think that is worth clearing up, although it may be a little tedious. However, my explanation of it should serve as "buyer's guide" if you are hesitating over exactly what to order.
In 1948 the Golden Cockerel Press issued an "edition-de-luxe" of translations from Medieval Welsh prose tales, made by Gwyn Jones and Thomas Jones, under the title of "The Mabinogion." This was the direct ancestor of the present Everyman volume. The translators, besides sharing a common Welsh name, were both distinguished academics: Thomas Jones was Professor of Welsh at Aberystwyth, and Gwyn Jones was Professor of English at Aberystwyth and Cardiff.
This title of the book was, as the translators pointed out, an erroneous form, a mere scribal error turned into a comprehensive title for stories with quite diverse histories. It was established in the public mind in the nineteenth century by Lady Charlotte Guest, who issued the first complete English translation of the stories, with Welsh texts, published in seven volumes, 1838-1845. The English text and notes of the shorter 1848 edition of her version had been included in the "Everyman's Library" series since 1906. This fat (432 pages) little volume furthered its position with the literary public interested in Welsh matters, general Celtic literature, or Arthurian stories, despite enormous advances in Welsh studies in the intervening century before the Jones and Jones translation. (I have separately reviewed some of its recent editions, with more on the translator's remarkable life.)
A more accurate translation by T.P. Ellis and J. Lloyd, "The Mabinogion: A New Translation," had been published by Oxford University Press in 1929, and seems to have made little impact. (One wonders: did the Depression play a role?) It had some useful annotations, and I have often wondered why it has never been reprinted, while Guest has gone into a variety of fuller or shorter versions (including the stories-only Dover Thrift edition, and one, apparently with the notes, illustrated by Alan Lee) of her bowdlerized and otherwise truncated rendering. Ellis and Lloyd continued to use Guest's title, and omitted one story, "Taliesin," a practice which Jones and Jones followed with no clear explanation. (I will offer one below.)
Otherwise, the narrative contents of all three of these translations are the same. They contain stories in four categories. (Note that preferred spellings of proper names vary, and I have not tried to be fully consistent.)
First, "The Four Branches of the Mabinogi," from which the collective title was derived, consisting of "Pwyll, Prince of Dyved," Branwen Daughter of Llyr," "Manawydan Son of Llyr," and "Math Son of Mathonwy." These begin with a story about the conception and birth of Pwyll's son, Pryderi, whose death is one of the early events in the "Fourth Branch," and concern a variety of heroes, and what are clearly rationalized gods. (Evangeline Walton turned each of the "Four Branches" into a novel; and other writers have done versions of one or another of them.)
Second, there are two "native tales," "The Dream of Maxen Wledig" and "The Story of Lludd and Llevelys," about Roman ("historical") and pre-Roman ("mythical") Britain as imagined by the medieval Welsh. The 'Lludd" text, as we have it, actually belongs to the "Chronicle" tradition launched by Geoffrey of Monmouth's supposed translation from an "ancient British book." (Which, if any part of it ever had any existence, was NOT the "Mabinogion.") "Maxen" seems to reflect an even more garbled version of a story known to Geoffrey, compounding several real people.
Third are two Arthurian stories in native Welsh mode. "Culhwch and Olwen," is an elaborate quest, dragging in, at least by name, most of the gods and heroes traceable in Welsh material, and some of their Irish cousins into the bargain, mostly as part of Arthur's court. "The Dream of Rhonabwy" is a visionary encounter with Arthur and his warriors (and anything else I could say would probably be controversial); a fascinating text, which almost boasts of its authentically dreamlike obscurity.
Fourth are three "Romances," "Owain" (otherwise known as "The Lady of the Fountain"), "Peredur son of Evrawc," and "Gereint the Son of Erbin," the first and last of which are clearly versions of Chretien de Troyes' Old French Arthurian Romances, "Yvain" and "Erec," while the second is related in a more complex manner to his unfinished and problematic "Perceval le Gallois." These seem to illustrate Celtic materials going out into wider European society, and then flowing back into Wales to enrich (and confuse) the native heroic and mythic tradition with ideas of chivalry.
The story missing from these two later translations, as well as a third version from 1976, was published by Charlotte Guest as "The Tale of Taliesin," although it is also found in some manuscripts as two separate tales. Although attested rather late, there are Irish parallels, and its tradition would seem to belong very much with the "native tales" like the "Four Branches of the Mabinogi" and "Culhwch." There seems to have been a real Taliesin, an early medieval poet, to whom much later poems were also attributed, but this story-complex has more to do with the myths about the nature of poetry. (It is also behind Thomas Love Peacock's comic novel, "The Misfortunes of Elphin," and quite a bit of modern fantasy literature.)
Fortunately for those of us who do not read medieval Welsh, Everyman's Library retired the lovely, but unreliable (and textually dubious) Guest translation, replacing it with Jones and Jones in 1949 (J.M. Dent and Sons, Ltd., London, and E.P. Dutton & Co., Inc., New York). This was an inexpensive and readily-available edition, which included a set of textual notes. Confusingly, it kept the old series number (97), which can lead to problems when ordering used copies. It was frequently reprinted, sometimes with emendations including a reissue in 1974 with Supplementary Textual Notes. This preserved the old pagination, which was frequently cited in discussions of the stories, but made it necessary to check the Supplement to be sure of the translators' most recent conclusions. It appeared with more revisions, additions, and a welcome Index of Proper Names in 1989. There were paperback editions (No. 1097) with at least two different covers, one lovely, one, to my mind, merely garish.
Finally, in 1993, with Dent now part of the Orion Publishing Group, and Charles E. Tuttle as the American publisher, it was reset for the Everyman Paperback Classics, with the changes to the translation smoothly incorporated, and the Textual and Supplementary Textual Notes in what seem to be their final forms. Gwyn Jones was still alive to work on these revisions, now with the collaboration of his wife, Mair Jones. The new pagination makes it harder to locate older references to passages; I have held on to my copies of older printings for this reason. Why go flipping through pages when I can look up the reference directly, and then find the corresponding section in a few seconds?
There is also a hardcover edition with a Preface by John Updike, published under the Borzoi imprint in 2001 (not seen). However, as the 1993 / 2001 text is the translator's final, preferred, revision, it is important to know that there is a difference -- especially if you are ordering it used. The 1974 text still had, besides the 44-page introduction, 283 pages. The 1993 edition, and its reprintings, are in a slightly larger format, and have a 32-page introduction, and 240 pages of main text.
Jones-and-Jones is in almost every way superior to the Guest translation, and is readily available; the lack of the "Taliesin" material, and of comparable, but modern, annotations, are its only failings. It has two modern competitors. One is the Penguin Classics "Mabinogion," translated by Jeffrey Gantz. The English of this translation is more modern, and some prefer it. I find Gantz's decisions on spelling some of the Welsh names rather strange; and some students of Welsh think that some of them are hard to justify. Of more importance to most readers will be his decision to give many of the names, particularly in the long lists of champions, their wives, dogs, horses, and swords, in "Culhwch," in the original Welsh. That sounds normal enough, but they are often intended to be understood as nicknames, whose meaning should be transparent, not meaningless, and some are even funny ("Big-bone, daughter of Strength"). Gantz consistently translates them in footnotes, which is highly distracting. In many cases, putting the Welsh text there for those who need it would have kept the main text easier reading, and looking less like the "begats" in "Genesis" and "Numbers.".
The other alternative -- which I would suggest getting as a supplement to either, if not, indeed, as a first choice -- is Patrick K. Ford's "The Mabinogi and Other Medieval Welsh Tales." It drops the French-influence Romances, the enigmatic "Rhonabwy," and "The Dream of Maxen," but gives a clear and vigorous rendering of the Welsh material, with an excellent introduction and notes. Ford not only did away with the persistent "Mabinogion" mistake in the title, he also included "Taliesin," based on the text he had re-edited from manuscripts, and restored to its two-story version, as "The Tale of Gwion Bach" and "The Tale of Taliesin."
It seems that Ellis and Lloyd and Jones and Jones, knew that Charlotte Guest's text for the story (with poems) had passed through the hands of the notorious Iolo Morganwg. He was a pioneering scholar who didn't hesitate to *invent* the evidence to support his theories, and they had preferred not to plunge into that thicket. Nor had anyone else. Unfortunately, the Guest version had been worked over by Robert Graves for his brilliant, and absurd, "The White Goddess," and a reliable version for non-Celticists was more than overdue. Ford's text edition was of value for another reason; there are close parallels between the stories of Gwion and the boyhood of the Irish hero Fionn (Finn McCool), investigation of which certainly needed a proper edition of the Welsh version to work from.
As an added bonus, Ford included as an appendix a translation of the notoriously difficult "Cad Goddeu," or "Battle of the Trees," also found in Guest's notes. It too had been given a splendid, and absurd, interpretation in terms of the Irish Ogham script by Robert Graves, who demonstrated his profound lack of knowledge of Welsh, and equally deep understanding of Irish. (He actually "improved" and re-ordered the translation he was using, without reference to the original....) Ford doesn't claim to understand its "real meaning," if any, only what it actually says, and it is very nice to have it. (By the way, "The Battle of the Trees" seems likely to have been in Tolkien's mind, along with Birnam Wood coming to Dunsinane, when writing of the Siege of Orthanc.)
There is a growing secondary literature about the "Mabinogion" stories, ranging from the excellent but technical, to the trivial, to the seriously erroneous (Graves is not alone!). Gwyn Jones himself contributed an excellent, and readable, analysis of "Culhwch and Olwen," in his book "Kings, Beasts, and Heroes" (1972), where it joins "Beowulf" and "Hrolf Kraki's Saga" (Jones having also translated the latter).