Bromwich, Rachel, and D. Simon Evans. Eds. and trans. Culhwch and Olwen: An Edition and Study of the Oldest Arthurian Tale. Aberystwyth: University of Wales, 1988; Second edition, 1992. ISBN Study. The second edition has the Welsh text, but the Introduction and Notes are in English. There’s no translation of the tale, but there is a glossary and the notes are quite helpful.
Amazon UK catalog page for Culhwch and Olwen: An Edition and Study of the Oldest Arthurian Tale
Bromwich, Rachel. Ed. and trans. Trioedd Ynys Prydein: The Welsh Triads. University of Wales Press: Cardiff, 1978; Second edition 1991. Third edition 2004. A standard resource, Bromwich includes an Introduction, notes, all the triads in Welsh and in English, and various indices of names,
Ford, Patrick K. Trans. The Mabinogi and Other Medieval Welsh
Tales. Berkeley: University of California Press, 1977. ISBN 0520034147. Ford doesn’t include the romances, but he includes the four branches, the native tales, and Taliessin material that is not available elsewhere in English. I think his introduction alone is worth the price of the book, and his translation is faithful to the tone of the Welsh, and easier to enjoy than any other.
Ford, Patrick K. “Prolegomena to a Reading of the Mabinogi: ‘Pwyll’ and ‘Manawydan.'” Studia Celtica XVI/XVII (1981-82): 110-25. This is a provocative analysis and very close reading of the first branch.
Ford, Patrick K. “Branwen: A Study of the Celtic Affinities.” Studia Celtica XXII/XXIII (1987/1988): 29-35. This is a close reading of the second branch, against a backdrop of Celtic myth and the rest of the branches.
Gantz, Jeffrey. Trans. The Mabinogion. London and New York: Penguin Books, 1976. ISBN 0140443223. Welsh names are difficult for non-Welsh speakers and it makes no sense for Gantz to introduce a new wrinkle by using non-standard spellings like Mallowch for Matholwch. I also think his introductions don’t really offer as much as they should to a new reader. However, he does succeed in presenting the Mabinogi in a modern English translation. Either Gantz or Jones is a good companion to the Ford Mabinogi.
Hamp, Eric P. “Mabinogi.” Transactions of the Honourable Society of Cymmrodorion (1974-1975): 243-249. Hamp has come with what most consider the best explanation of mabinogi “the materials, or doings pertaining to (the family of) the divine Maponos.” Hamp further theorizes that the four branches as we have them are the story of the father of Maponos, Gwri/Pryderi.
Jones, Gwyn and Thomas Jones. The Mabinogion. Everyman’s
Library 1949; revised in 1989, 1991. ISBN 0460872974. This is the first English translation after Lady Charlotte Guest’s “literary” version in the previous century, and is still the standard translation of all the texts in the so-called Mabinogion. It includes the Four Branches, the Romances, and the four native tales.
Mac Cana, Proinsias. Branwen, Daughter of Llyr: A Study of the
Irish affinities and of the Composition of the second branch of the
Mabinogi. Cardiff, University of Wales Press, 1958. Some
interesting parallels between the Welsh second branch, and various Irish texts.
Rees, Brinley and Alwyn Rees. Celtic Heritage: Ancient Tradition in Ireland and Wales. New York: Thames and Hudson, 1961; repr. 1989. ISBN 0500270392. A super introduction and overview of the mythological medieval Irish and Welsh literature, from a comparative (Dumezielian and occasionally quirky) point of view.
Amazon catalog page for Celtic Heritage: Ancient Tradition in Ireland and Wales
Amazon UK catalog page for Celtic Heritage: Ancient Tradition in Ireland and Wales
Sullivan, C. W. III. Ed. The Mabinogi, A Books of Essays. New York: Garland Publishing, Inc., 1996. ISBN 0815314825. This is a collection of essays that have been reprinted from various accademic scholarly journals, some of them quite hard to find. It’s a well done collection, with most of the central articles included. It isn’t cheap, (it lists for about $80.00) but it is very thorough. You might want to try interlibrary loan if your local branch doesn’t have it.