I must admit that I know very little about Celtic Mythology. It is a time that I have always thought I would liked to have lived in though. Could anyone tell me a good place to start reading the Celtic Myths?
A new book by MacKillop called Myths and legends of the Celts is very interesting and thorough.
If you want something a little less heavy and more concentrated on nice retellings of the basic myths, try the classic by Rolleston:
Myths and legends of the Celtic Race. Or Celtic Myths and Legends by Charles squire.
Visit your local library, its easier sometimes than trying to look everything up online. I did this for a few things and sometimes I find sites that contradict others. For me sometimes when the topic is so stuck in my head, the only way I can clearly learn more is in a quiet place.
If you're interested in legends about King Arthur, you might seek out various treatments of the Celtic King Arthur. The Brythonic branches of the Celts treated him differently than did the Gaelic branches. Both groups claim him and have legends that grew out of the Arthurian tradition. An easy modern-day fictional way to start is with White's "The Once and Future King" and working your way through a more modern version such as "The Mists of Avalon." I loved the Celtic mythology from the woman's point of view, as in "Mists."
I've read much of the earlier Arthurian literature. I enjoyed Mallory (15th C.), and recently read Tennyson's Idylls of the King.
I have not yet made it to White.
My favorite stories are Yvain, or the Knight with the Lion by Chretien Des Troyes(12th C.),
and the middle English Sir Gawain and the Green Knight.(I think 14th C.)
My favorite Arthurian novel is Parzival by Wolfram von Eschenbach. It is mostly about the Grail Quest, but it incorporates less Christian mythology than Mallory or most other writers on the subject (not that I don't enjoy Christian mythology ). Parzifal is more like an ordinary bloke than someone like Galahad, whose saintliness and disdain for the world is not exactly endearing. Moreover, Wolfram's Grail is not the Cup of the Last Supper but a green meteorite. By the way, there is a fascinating retelling of Parzival by the novelist Lindsay Clarke, which incorporates a Jungian perspective. It is a much easier read than Wolfram's original version. Highly recommended if you are not allergic to a slight(!) psychological bias. After all, as everyone knows, the Holy Grail obviously is not really out there somewhere. The Grail legends are metaphors of an inner quest. I can't explicate this mystery in a nutshell, no one can. That is the reason for all the literature about it: attempts to explain the unexplainable.