Introduction to Welsh Mythology
At the beginning let me say that my knowledge of Welsh mythology is very limited. I’ve always had more affinity for Ireland (as this is the land of my father’s ancestors) and have always concentrated on it. Writing about Welsh mythology is more about general knowledge than actual interest in study. So the aim of this essay is to take a general look at what we mean when we say Welsh Mythology. (A full list of Welsh Mythology Texts)
As soon as anyone says the words Welsh Mythology everyone automatically thinks of two things, first, The Mabinogian, and second The Barddas. However, are they all there is to Welsh Mythology? My answer (after a bit of research) would an emphatic NO!
From my previous essay on Celtic Mythology, we know that none of the Welsh writings from the first millennium survived intact. There are fragments in Old Welsh that date to the ninth and tenth century CE. And the medieval manuscripts that survived when looked at linguistically can also be dated to the oral traditions of the ninth and tenth century CE.  Most of the Welsh mythology though came to us in the form of Middle Welsh manuscripts. The manuscripts are: The Book of Aneurin, The Book of Taliesin, The Black Book of Carmarthen, The White Book of Rhydderch and the Red Book of Hergest and the White Book of Hergest. Other sources include the ninth century Latin text History of the Britons, Geoffrey Monmouth’s twelfth century Latin text History of the Kings of Britain and later works of folklore like the Welsh Fairy Book by W. Jenkyn Thomas written in 1908. There are also mnemonic list-texts like the Welsh Triads and the Thirteen Treasures of the Island of Britain. 
I’m going to begin by taking a closer look at the manuscripts.
The White Book of Hergest, to be distinguished from the Red Book of Hergest, dates from the mid-fifteenth century CE and was destroyed by a five in the nineteenth century. Among its contents were the laws of King Hywel Dda.
A great collection of medieval Welsh prose, the White Book of Rhydderch was copied on parchment around 1325 CE. It contains versions of the Mabinogi and all other narratives including the Mabinogion (except The Dream of Rhonabwy) and many religious texts. 
The Red Book of Hergest dates to around 1382-1410 CE, and is considered one of the most important of all the medieval Welsh manuscripts. It contains texts of the Mabinogi and the seven other narratives usually included in the Mabinogion. The Red Book also has poetry of the Godynfeirdd (poets of the twelfth to early fourteenth century CE), histories, grammars, and proverbs, but not religious works or laws. 
The Book of Aneirin was transcribed in the middle of the thirteenth century. Twenty percent of the manuscript can be dated linguistically to the ninth and tenth century CE. The manuscript contains the poem Gododdin. 
Compiled in the fourteenth century CE, the Book of Taliesin contains more than sixty poems attributed to the sixth century Taliesin. Of these sixty only twelve were really thought to be his. The manuscript also includes Prophecy of Britain, attributed to Myrddin (Merlin) and Cad Goddeu. 
The Black Book of Carmarthen is considered to be the earliest complete manuscript of Welsh poetry. It was transcribed around 1250 CE. The manuscript includes a large number of poems datable from the ninth to the end of the twelfth centuries. Many of the poems were about heroes and some were in the voice of Myrddin. 
Now I’m going to talk a little about the more famous myths of the Welsh mythology and that is the two texts of the Mabinogian and the Barddas.
The Barddas of Iolo Morganweg is a visionary reconstruction of the Druidic and Bardic tradition, which had and still has a huge influence on the modern Celtic and neo-Pagan revival, or a notorious forgery. Actually both statements are very true… Iolo Morganwg, who was born Edward Williams, was a native speaker of both English and Welsh. He spent his entire life collecting and transcribing medieval Welsh documents, as well as writing poetry under his own byline. He was also a first-rate literary forger of ancient Welsh; some have commented that his forgeries were as good or better than the real thing. It is also true that he wrote much of the Barddas under the influence of laudanum (an opium-based medication which he took for asthma).  No one can deny though that even though almost everyone knows it is a forgery the Barddas is now considered a part of Welsh mythology by a lot of Neo-pagans and Neo-Druids.
The most mythological stories contained in the Mabinogion collection are collectively titled The Four Branches of the Mabinogi. The Mabinogi is all about the life of the hero Pryderi. He is conceived, born and named in the first Branch, fights for Bendigeidfran in Ireland in the second, loses and regains his kingdom in the third, and dies in the fourth. He was probably originally central to all four Branches, and remains so in the first and third, but is reduced to a passing mention in the second and fourth, which concentrate on the children of Llyr and the children of Dôn, two clans of characters who were probably once gods. 
Two of the most famous poems of the Welsh mythology are Cad Goddeu or The Battle of the Trees and Y Goddodin. The Battle of the Trees talks about how the legendary enchanter Gwydion animates the trees of the forest to fight as his army , while the Goddodin is a series of elegies to the men of the Britonnic kingdom of Gododdin and its allies who, according to the conventional interpretation, died fighting the Angles of Deira and Bernicia at a place named Catraeth. 
I hope this short introduction to Welsh mythology is a helpful one to all who want to study it and find it a guide to where to start.
 “Welsh Texts” Access Date: January 27, 2010 http://www.maryjones.us/ctexts/index_welsh.html
 “Welsh Mythology” November 2, 2009. Access date: January 27, 2010. http://en.wikipedia.org/wiki/Welsh_mythology
 James Mackillop. Oxford Dictionary of Celtic Mythology. (New York: Oxford University Press, 2004) p.428
 Ibid, p. 371
 Ibid, p. 47
 Ibid, p. 49
 Ibid, p. 43
 “Iolo Morganwg” January 12, 2010. Acess date: January 28, 2010 http://en.wikipedia.org/wiki/Iolo_Morganwg
 “Mabinogion” January 27, 2010. Access date: January 28, 2010 http://en.wikipedia.org/wiki/Mabinogion
 “Cad Goddeu” December 29, 2009. Access Date: January 28, 2010 http://en.wikipedia.org/wiki/Cad_Goddeu
 “Y Gododdin” January 27, 2010. Access Date: January 28, 2010 http://en.wikipedia.org/wiki/The_Gododdin