I only just remembered that this book exists; when I was a little kid, I re-read this probably once a month. I cannot think of any book that carries as much nostalgia for me as this one.
I can't remember every story it included off the top of my head, and I don't have my copy within reach, but I'll list the ones I recall:
*The Sampo, from the Kalevala, involving Lammenkainen and Vainamoinen battling Queen Louhi
*The legend of Sundiata
*Beowulf's conflicts with Grendel and the dragon
*A story involving Sir Caradoc
*Sir Gawain and the Green Knight
*A legend involving how seals came to exist
*Saint Martha and the Tarasque
*A story of two kids outsmarting a witch; not Hansel & Gretel, but a bit similar
*A story involving a man who could transform into a lion
*Theseus, Ariadne, and the Minotaur in the Labyrinth
I am certain that I have forgotten more of the stories than I have recalled here; I intend to track down my copy and read it again soon, to see how well the stories held up over time for an adult reader.