There are two styles of demi-glace. One is "classic," and the other is "modern."
The classic demi-glace is always espagnole mixed in equal proportions with veal, beef or chicken stock and reduced by 50%. The veal stock version is called demi-glace, the chicken version is called chicken demi-glace, and the beef version is called regular, normal or brown demi-glace. As you can imagine the terminology differences between veal and beef are honored more in the breach than in actuality. They are used more or less interchangeably.
To make an espagnole, saute some mirepoix in butter until it just begins to show color. Add some flour and cook it slowly until it forms a brown roux. Push it to one side, and put a little tomato paste on the bottom of the pan. Cook the paste until it darkens and the "raw" is fully cooked off. Mix the roux and the paste to form a pincage. Add some veal stock and reduce by 25%. The final reduction should be nappe consistency. An espagnole, on it's own does not taste very good.
Modernly, demi glace is often made as a simple reduction of veal or beef stock, skipping the espagnole entirely. Julia Child famously called this method a "semi-demi glace." The reduction factor is about 2/3 and should be undertaken fairly slowly.
I learned most of what I know about classic sauces from "Modern French Culinary Art" which is aka "The Great Book of French Cooking" by Henri Pellaprat. It was originally written in the thirties, and is still in print. I recommend buying the edition from the seventies. It is the most complete and the best illustrated.
There's pretty much a consensus that the best sauce books -- textbooks really -- are, "Sauces: Classical and Contemporary Sauce Making" by Peterson, and "The Sauce Bible: Guide to the Saucier's Craft" by Larousse. If you have to choose one, choose Peterson.