I make no apology for providing a précis in the previous part of the Fourth Branch of the Mabinogi, named from Math son of Mathonwy, here. It is often described as the most complex of the four branches and is certainly the most mythological, containing shapeshifting in abundance, featuring the Children of Don.
It has been suggested that The Mabinogi Math is a retelling of the legend of the King and his Prophesised Death and not Celtic in origin, but a universal legend told in Egypt, Greece and the middle East in addition to Ireland and Wales.  Recently scholars have suggested that Mabinogi Math maybe an interpretation of a pre-Christian creation myth based on the etymology of the name Don being cognate with Old Irish don = “place, ground, earth”, i.e. Children of the Earth. 
Math was the brother of Don and son of Mathonwy, a great and wise king, ruler of Gwynedd, uncle to Gwydion, Gilfaethwy and Arianrhod, and brother of Penarddun. He had the strange gift of hearing everything that was said once the wind took hold of it. This same gift was said to have been possessed by the Coraniaid, a supernatural race listed in the Triads as one of the Three Oppressions and one of the three plagues of Lludd’s reign, as we saw in Lludd’s Dragons (Part VII.) This plague was eradicated by bruising insects that he had obtained from his brother Lleuelys in France, and sprinkling this concoction over the Coraniaid.
The name Math is derived from the Proto-Celtic *matu- meaning "bear”, providing the root of the Gallic god Matunus, a Latin form of the Celtic Matunos, who was known to have been worshipped in Roman Britain from an altar stone dedication at High Rochester dating from AD213. This god clearly indicates a relationship to Artos as the two ancient Celtic words for bear were math or matu and art or artos. We know that there was a bear cult worshipped in ancient times and in Gaul there was a divinized she-bear, called Dea Arti. There were many gods assimilated to the god Mercury; the Bear God ‘Artaius’ (from which the Celtic god Arthur is ultimately derived) was one such known as Mercury Artaius, and widely worshipped by the continental Celts.
It has been proposed that Math is a corruption of Welsh Mathien, from Irish Mathgen, meaning relative (or kin) of the bear and the epithet Mathonwy an adaptation of the Irish name Mathgamnai, literally ‘bear cub’, and in Gaulish we find matugenos meaning ‘son of the bear’s son,’ therefore a suggested meaning for Math vab Mathonwy would be "Bear-kin, son of the Bear cub".
The setting of the Fourth Branch is Gwynedd in North Wales and portrays Math as the great sorcerer king of Gwynedd, but the main focus is on his nephew the wizard Gwydion. There is some debate whether Mathonwy denotes the name of Math’s mother or father, as Gwydion presumably carries his mother’s name, Gwydion vab Dôn it is probable that it is a matronymic indicating a maternal lineage in the ruling house of Gwynedd.
The Trioedd Ynys Prydain name Math as one of the 'Three Great Enchanters of the Island of Britain' and goes on to say that he taught these enchantments to his nephew Gwydion, the powerful magician, come trickster, of the Fourth Branch who can create horses and hounds from toadstools, shoes from seaweed, illusions of an invading fleet and a woman out of flowers. The Triad states that Math taught these skills to Gwydion:
Three Great Enchantments of the Island of Britain.
The Enchantment of Math son of Mathonwy and he taught it to Gwydion son of Dôn.
And the enchantment of Uther Pendragon and he taught it to Menw son of Teirgwaedd.
And the third was the enchantment of Rudlwm the Dwarf and he taught it to Coll son of Collfrewy his nephew.
The great magician Gwydion’s name contains the form, gwyd- of the verb gwybot ‘to know.’ The word "gwyddion" can mean "trees" or "forest", (which is related to the word “goddeu”), the name could possibly mean "one born of wood," a suggested meaning of his name would be “woodwise”, and implies a man of learning who gained his learning from nature, a druid.
Gwydion may also be derived from *Uidugenos which in archaic Welsh is Guidgen, as found in the Brycheiniog genealogy contained in the Harleian 3859 manuscript; "Lou hen map Guidgen" (Lleu son of Gwydion). *Uidugenos is clearly very similar to Uiducus/Viducus, raising the possibility that Gwydion and Uiducus are essentially the same name. We find Uiducus as the deity Mercury Uiducus, meaning either "Mercury the Woodsman" (uidu- "wood, tree") or "Mercury the Wise" (uid- "see"). This would appear to confirm Gwydion’s divine status. 
Battle of the Trees
Gwydion is mentioned in the poems "The Chair of Cerridwen" and "Song Before the Sons of Llyr.” Math and Gwydion also feature as the wizards in the poem The Battle of the Trees (Cad Goddeu) also from the 14th Century Book of Taliesin, in which they turn trees and shrubs to form an army. This poem is generally thought by scholars to be the battle from the Arthurian Battle list in Nennius, Chapter 56, Cat Coit Celidon in a mythological context and given a northern location based on the location of Goddeu in Rheged, roughly an expanded modern day Cumbria. This mythological battle is often cited in a contradictory context to locate a historical Arthur.
This poem, The Battle of the Trees, although usually referred to as one of the bard Taliesin’s boasting poems, is clearly recounting Math and Gwydion’s battle with Pryderi son of Pwyll over the pigs stolen from Annwn (Dyfed). It contains sections referring to episodes we see in the The Fourth Branch; the creation of Bloduedd from flowers and mentions Math, Gwydion, Dylan and Goronwy, even a possible allusion to Lleu as an eagle. It would seem to be based on the, now lost, same pagan original tale as the Fourth Branch, centred on Gwynedd and the Lleyn Peninsula in particular, exactly where we find the Children of Don located. 
A short poem found in the later manuscript (Peniarth MS 98B) confirms the fact that the Battle of the Trees (sometimes called The Battle of Achren), was fought over animals that had been stolen from the otherworld by the Children of Don. The account describes how Amathaon ab Don brought a white roebuck and a welp from Annwn and fought with Arawn, King of Annwn. Gwydion sang the two Englyns following:
"Sure-hoofed is my steed impelled by the spur;
The high sprigs of alder are on thy shield;
Bran art thou called, of the glittering branches."
"Sure-hoofed is my steed in the day of battle:
The high sprigs of alder are on thy hand:
Bran by the branch thou bearest
Has Amathaon the good prevailed."
The Battle is referred to in the Triads of the Island of Britain:
Three Futile Battles of the Island of Britain:
One of them was the Battle of Goddeu: it was brought about by the cause of the bitch, together with the roebuck and the plover;
The second was the Action of Arfderydd, which was brought by the cause of the lark's nest;
And the third was the worst: that was Camlan, which was brought about because of a quarrel between Gwenhwyfar and Gwennhwyfach.
This is why those (Battles) were called Futile: because they were brought about by such a barren cause as that.
The Four Branches were likely based on an original, now lost, tale detailing the conflict between the Children of Don in the North of the Children of Llyr from the South, concluding in the final battle (of the Trees) for the magical creatures stolen from Annwfn, resulting in Pryderi's death, which Gwydion brings about by way of getting Math to leave Caer Dathyl so that Gilfaethwy can have his way with Goewin.
The Battle for the Pigs
In the Fourth Branch Gwydion tells Math that he had heard that a certain type of creature had come into the South, which has never come to this Island before:
'What is their name?' asked Math.
'What kind of animals are those?'
'Small animals, their meat is better than the meat of oxen. They are small and they are changing names. "Pigs" is what they are called nowadays.'
'To whom do they belong?'
'Pryderi son of Pwyll, sent to him from Annwfn by Arawn king of Annwfn. 
In this story, pigs make their first appearance as a gift from Arawn, lord of the Otherworld, to Pwyll, who then passed them on to his son Pryderi. Here we see an indication that pigs had a particular connection to Annwfn, and a special status as a cult animal amongst the Celts.
The story of the seven pigs which Arawn gave to Pwyll, Lord of Annwfn, are now the property of Pryderi, the swineherd and mentioned in the Triads:
Three Powerful Swineherds of the Island of Britain:
Pryderi son of Pwyll, Lord of Annwfn, tending the swine of Penndaran Dyfed his foster-father. These swine were the seven animals which Pwyll Lord of Annwfn brought and he gave them to Penndaran Dyfed his foster-father. And this is the place where he used to keep them, in Glyn Cuch in Emlyn. And this is why he was called a powerful swineherd: because no one was able either to deceive or to force him.
And the second was Drystan son of Tallwch, tending the swine of March son of Meirchyawn, while the swineherd went with a message to Essyllt. Arthur and March and Cei and Bedwyr all four were there. But they did not succeed in seizing even one pigling, not by force, nor by deception, nor by stealth...
In the opening lines of the First Branch of the Mabinogi, Pwyll is his chief court at Arberth and decides to go hunting at Glyn Cuch, he set out that evening from Arberth, coming as far Pen Llwyn Diarwya, and spent the night there. The next day he came to Llyn Cuch, and while out hunting when he comes across another pack of hounds bringing down a stag, the dogs have dazzling bright white and with red ears. These are no doubt the hounds of hell, the cwn annwfn, the hounds of the Wild Hunt. Pwyll argues over the stag with the other huntsman, who says he is “From Annwvyn. Arawn, king of Annwfn am I.'”
Arberth has been been identified with Narbeth in Southern Pembrokeshire and the location of Glyn Cuch in Emlyn is almost certainly modern day Newcastle Emlyn, in the Teifi Valley, spanning across the county borders of Ceredigion and Carmarthenshire in west Wales. Lying on the River Teifi, Emlyn was one of the seven cantrefs of Dyfed, the name derives from am (around, as on both sides of) and glyn (valley); the valley in question being the Cuch which provided the border of the commotes of Emlyn Is Cuch (to the west) and Emlyn Uwch Cuch (to the east).
After trading the twelve horses, hounds and shields that Gwydion had created by magic from toadstools, they swiftly left as the magic would not last from one day to the next. After leaving Pryderi’s court in Rhuddlan Teifi (near Lampeter in Ceredigion), the trail of the pig drive back to Gwynedd can be traced through the pig (moch) place-names of the text:
Mochdref – probably Nant y Moch in the uplands of Ceredigion.
Mochdref - over Elenid, between Ceri and Arwystli. Southwest of Newtown, Powys
Mochnant - Commote in Powys
Mochdref - near Colwyn Bay, Rhos.
Creuwyon (Cororion), - where a sty was made for the pigs at the highest township of Arllechwedd.
Math's army waited for Pryderi’s forces at Pennardd. Gilfaethwy and Gwydion slipped away to Caer Dathyl that night and Goewin was taken against her will. The two armies faced each other between Maenawr Bennard and Maenawr Coed Alun (Coed Helen). According to local tradition, Gwydion stood on a hill to watch and direct the battle, Bryn Gwydion, is near Clynnog off the A499, South of Caernarfon.
Pryderi’s army retreated, culminating in the final battle, and Pryderi’s death, at Traeth Mawr, (Aberglaslyn was a tidal estuary then, prior to the building of the Cob at Porthmadog). Pryderi was killed in single combat against Gwydion’s magic and buried at Maentwrog.
And so ends the original tales of Pryderi.
However, the Fourth Branch goes on from this point to tell the tale of Lleu.
The Tale of Lleu
As Goewin was no longer a maiden, Math had to find another, and in failing her test Aranhod promptly dropped Dylan and Lleu, the divine twins. Aranrhod appears in the Book of Taliesin and is famed for her beauty. She appears in three Triads, her father mentioned as Beli, and in the Fourth Branch her mother is the goddess Don. She is without doubt a deity, traditionally her name meaning “Silver wheel” which may indicate she was the goddess of the moon. However, Aranrhod’s name is originally and consistently spelled Aranrot, which would mean ‘big, round wheel’ giving astronomical connotations of the zodiac. She fails to recognise Lleu as her son and puts three curses on him. The identity of Lleu’s father is not revealed but Gwydion shows a keen interest in the boy, thus giving the innuendo of incest with his sister Aranhod.
Upon being baptised Dylan Eil Ton meaning “Prince of Wave”, or “Son of Wave” immediately made for the sea. Shape-shifting from human to animal form occurs often in this branch of the mabinogi, it has been suggested that that Dylan changes shape into an unnamed creature when he is baptized, possibly a seal, selkies being well known in Celtic mythology. 
Dylan appears in two poems in the Book of Taliesin, giving little away about his story:
From The Battle of the Trees:
I played in the twilight,
I slept in purple;
I was truly in the enchantment
With Dylan, the son of the wave 
The Death-song of Dylan, son of the Wave
ONE God Supreme, divine, the wisest, the greatest his habitation,
When he came to the field, who charmed him in the hand of the extremely liberal.
Or sooner than he, who was on peace on the nature of a turn.
An opposing groom, poison made, a wrathful deed,
Piercing Dylan, a mischievous shore, violence freely flowing.
Wave of Iwerdon, and wave of Manau, and wave of the North,
And wave of Prydain, hosts comely in fours.
I will adore the Father God, the. regulator of the country, without refusing.
The Creator of Heaven, may he admit us into mercy. 
The Fourth Branch mentions the blow by which his death was caused was cast by Gofannon, his uncle, the divine smith, deemed one of the Three Ill-Fated Blows, however the Triad has not survived. Gofannon son of Don, the divine smith, patron of metalworkers, also appears briefly in Culhwch ac Olwen as a gifted smith; one of the tasks given to Culhwch if he is to win the hand of Olwen is to get Gofannon to sharpen the plough of his brother Amaethon son of Don, the divine ploughman.
Gofannon also appears in the Book of Taliesin:
I have been with skilful men,
With Matheu and Govannon,
With Eunydd and Elestron,
In company with Achwyson,
For a year in Caer Gofannon. 
Matheu is clearly Math son of Mathonwy, but Caer Gofannon, the fort of the smith remains elusive and sadly the whole story of Dylan seems to have been lost and denotes a missing, much older mythological cycle.
>> Part XI - The Fair One with a Skillful Hand <<
1. W J Gruffydd, Math vab Mathonwy, University of Wales Press, Cardiff, 1923.
2. John Carey, Journal of the History of Religions 31, discussed in Celtic Culture by John T. Koch, 2006.
3. Considering that the word Druid (magician, priest) is thought to derive from "drus" meaning oak, it is likely that the word for scientist is derived from forest, i.e. the man of learning gained his knowledge from nature. – Gwydion by Mary Jones [http://www.maryjones.us/jce/gwydion.html].
4. Places mentioned in the Fourth Branch of the Mabinogi – The Nantlle Valley website [http://www.nantlle.com/mabinogi-saesneg-places-mentioned-in-the-fourth-branch.htm]
5. The Four Branches of the Mabinogi, Will Parker, Bardic Press, 2005.
6. Keefer, Sarah Larratt. 1989-1990. “The lost tale of Dylan in the Fourth Branch of The Mabinogi.” in C.W. Sullivan III (ed.) 1996. The Mabinogi: a book of essays. New York & London. 79-97.
7. Battle of the Trees (Cad Goddeu) from The Book of Taliesin VIII, The Four Ancient Books of Wales, W F Skene.
8. The Death-song of Dylan, son of the Wave, from The Book of Taliesin XLIII, The Four Ancient Books of Wales, W F Skene.
9. The First Address of Taliesin, from The Book of Taliesin I, The Four Ancient Books of Wales, W F Skene.
* * *