The Mabonogi (the name means alternately "a story for children" or "a bard's tale" depending on whose translation you prefer) are comprised of 4 branches, entitled "Pwyll", "Branwen", Manawydan", and "Math". Aside from these four branches there are another 8 individual tales in the British and French style. Taken together, these tales of heroes and stirring deeds depict a Celtic vision of enchantment and romance that moves effortlessly between the physical landscape of Wales and the Celtic underworld.
In some of the later stories King Arthur appears, though certainly not in the guise of the chivalrous knight known to modern readers. He is a giant, whose deeds involve ridding Wales of witches, monsters and other giants with aid of - no, not twelve knights, but his own band of hags, witches, and monsters.
To give you a flavour of the Mabinogion, I've included short summaries of several popular tales
The hero Eilhwch decides that he will find and wed this beautiful maiden, despite the warning that no one ever returned from such a quest alive. In order to win his love, Eilhwch is set a series of heroic (read impossible) tasks by Olwen's father. [Note the similarity to the Hercules myth - that hero was also set twelve seemingly impossible tasks to perform, which he proceeded to do.
Pwyll, Prince of Dyfed, took a fancy one day to sit on a mound at Narberth (North Pembrokeshire) which was said to presage strange adventures. Sure enough, he soon saw a lady dressed all in gold approaching upon a white horse. He sent his servants to fetch her, but no matter how fast they rode, she somehow managed to keep the same distance ahead of them.
Pwyll decided to pursue her himself, but again, no matter how fast he rode, he was unable to catch up to her. Finally, he called out to her, telling her that he loved her. Instantly she stopped, declaring with some humour that "it were better for the horse" that he called out sooner. The Lady Rhiannon said that her family was forcing her to marry someone against her wishes, but now she would have Pwyll or no-one. Sure enough, after many more adventures they were wed.
Bran, the King of Britain had a sister named Branwen, said to be the fairest lady in the world. Bran desired an alliance between Britain and Ireland, so he arranged a marriage between Branwen and the King of that country. The wedding, held at Aberffraw (in Anglesey), turned into a disaster when Branwen's brother insulted the Irish.
The Irish held their peace, but when they had treturned to Ireland, took revenge upon Branwen. The new bride managed to send a plea for help to her brother with the aid of a starling. The British took arms and invaded Ireland, and in the battle that followed almost all the warriors on both sides were killed. Branwen lamented in her grief, "Two islands have been destroyed because of me", and with that she died.
A note: Bran's castle is reputed to be at Harlech (not the much later Harlech Castle), or at Dinas Bran Castle, near Llangollen.
Manawyddan was a prince of North Pembroksehire whose lands fell under a mysterious enchantment which rendered the lands desolate. The prince discovered that a band of mice were eating his wheat, so he lay in wait for them one night. He managed to catch only one of the mice, which he decided to hang as a thief.
Before he could carry out the sentence upon the mouse, strangers began to come to house, offering to buy the mouse from him. Finally a man in the guise of a bishop asked him to name his own price for the mouse. Manawyddan, no fool, declared that the only price he would accept was the end of the spell upon his land. The "bishop" agreed, and revealed that he was, in fact, a rival prince named Llwyd.
Llwyd confessed that he had cast the spell when one of his friends was insulted by friends of Manawyddan. The mice who had been eating the crops were lords and ladies of Llwyd's court, and the mouse that Manawyddan had caught was none other than Llwyd's own wife.
Gwydion and Llew
Gwydion the hero had a son named Llew. Llew was married to the beautiful Blodeuwedd, who had been magically made for him from meadow sweet, broom blossoms, and oak. Blodeuwedd was unfaithful to Llew, and plotted to slay him with the aid of her lover, Gronw. Ah, but it is not easy to slay one who is the son of a god!
Llew could only be killed by a special spear if he was standing with one foot in a cauldron and the other foot upon a slain stag. Blodeuwedd tricked Llew into showing her the position, whereupon Gronw cast the spear. Llew turned into an eagle and flew far away. After a long search Gwydion found his son in Nantle (Caernarfonshire) and restored him to his human form with a magic wand. Gwydion then punished Blodeuwedd for her betrayal by changing her into an owl.
Maxen Wledig, Emperor of Rome
Maxen Wledig had a dream in which he beheld a beautiful maiden who sat upon a golden throne. When he awoke he sent his servants out far and wide, and eventually they found the maiden in Britain. The emperor hurried off to Caernarfon to woo and win the maiden for his wife. While he was absent from Rome his enemies siezed the throne. Maxen Wledig was able to regain power and defeat his foes with the help of his new wife and her friends.