The mother sauce that is typically used as a base for making a demi-glace is Espagnole sauce or brown sauce.
Demi-glace is a reduce of equal parts of Espagnole sauce and brown stock, that is simmered until it becomes a thick and intensely flavorful sauce,
Demi glace is often served with meats like duck meat, lamb meat or steak.
Espagnole sauce is a rich and dark brown sauce that is made from veal stock or brown beef, a dark brown roux of butter and flour cooked until very dark and mirepoix, "diced carrots, celery and onions", and tomato puree.
Espagnole sauce provides a deep and rich flavor base for other sauces.
And it's a foundation for demi-glace and several other classic French sauces, like Chasseur and Bordelaise.
To make Demi-Glace you mix Espagnole sauce with equal parts of brown beef or veal stock.
Then simmer the mixture uncovered, allowing it to reduce and also intensify in flavor until it is a thick and velvety consistency.
Once done the final product of demi-glace is a highly concentrated and flavorful sauce.
Demi-glace sauce is a basically a highly reduced brown stock, that is traditionally made from roasted beef or veal bones, mirepoix (onions, carrots, and celery), tomato paste, flour for the roux, and aromatics like garlic, bay leaves, thyme, and peppercorns.
Demi-glace sauce can also be made by combining a premade brown stock (like Espagnole sauce), which contains mirepoix, tomato, and roux, with more beef or veal stock and wine.