The five mother sauces are:

Hollandaise Sauce (butter, thickened with egg yolks)

some derivitives:

Bernaise - White wine or vinegar, diced shallots, tarragon, chervil 

Chantilly - add whipped cream

Maltaise – add orange juice

Choron - add tomato

Girondine - add mustard

Noisette - add Buerre Noisette

Bechamel Sauce (white - based on milk, thickened with a white roux)

some derivitives:

Mornay - the addition of Gruyere cheese (or any cheese you like)

Mushroom Sauce – add mushrooms

Sauce Allemande – add lemon juice

Sauce Américaine - white wine, brandy, salt, cayenne pepper and  butter

Suprême sauce – chicken stock, lemon and finely diced mushrooms

Veloute Sauce (blond – based on a white stock, thickened with a white or blonde roux)

some derivities:

Bordelaise - the addition of reduced red wine and poached beef marrow

Allemande Sauce - Veal veloute with egg yolk and cream liaison

Supreme Sauce - Chicken veloute reduced with heavy cream

Vin Blanc Sauce - Fish veloute with shallots, butter, and fines herbs

Espagnole Sauce (brown or demi-glace – based on brown stock thickened with a brown roux)

Lyonnaise - white wine, vinegar and onions

Bourguignonne sauce - reduced red wine with onions and parsley and thyme and butter

Chateaubriand sauce - veal stock, shallots, thyme, bay leaf, white wine, butter, lemon juice, parsley, salt,  pepper, and tarragon§         Chasseur - mushrooms, shallots, white wine (sometimes tomatoes and parsley

Sauce Robert - chopped onions cooked in butter, a reduction of white wine, pepper, an addition of demi-glace and is finished with a mustard 

Madeira - finely chopped celery, scallions, carrots, mushrooms, and herbs

Piquante - shallots, white wine, vinegar, gherkins, parsley Perigueux - with Madeira and truffles Charcutiere - chopped gherkins

Devile (diable) – garlic, shallots, steak sauce, dry mustard, black pepper, crushed red pepper

Mushroom – mushrooms, white wine, onion, garlic, thyme

Tomato Sauce (red - based on tomato plus stock, with an optional roux)

some derivitives:

Marinara (vegetarian) – olive oil, garlic, basil, oregano, parsley, red wine

Creole sauce – onion, celery, green pepper, garlic, salt, pepper, cayenne

Portuguese sauce – yellow onion, green pepper, green olives, thyme, cumin

Spanish sauce – onion, garlic, green chilies, jalapenos

Some thickening agents:

Roux

Egg Yolks

Flour

Cornstarch

Beurre Manie

Cream

Cheese

Tapioca

Arrowroot

Ground Nuts or Other Solids

Making the perfect ROUX:

A roux is equal parts flour and fat.  Any cooking fat can be used to prepare a roux, including butter, chicken fat, or bacon fat.  Typically 1 tablespoon of roux will thicken about 1 cup of liquid.  You can add a little roux at a time to gauge the thickness that you desire.  Keep in mind that sauces thickened with a roux will thicken as they cool.

Here are a few other sauce-thickening techniques:

Monter au beurre

This is a French term which means to finish a sauce with butter. As the last step in making a sauce, you add chunks of cold unsalted butter one at a time.  Whisk until the butter is melted.  This will give the sauce a rich flavor and a velvet-like texture.

Beurre manié

This is a mixture of flour and butter.  It is added for a quick and easy thickening at the end of the cooking process.  Add 2 ounces of flour to 3 ounces of softened butter. Mix into a paste using a wooden spoon.  If you are not using immediately this will hold well in the refrigerator.  

Liaison

This is a mixture of egg yolks and cream, used to thicken sauces and soups.  Add 3 egg yolks (beaten well) to one cup of heavy cream.   Add a small amount of the hot sauce or soup to the liaison to gradually increase the temperature.  Once it is tempered you can add it to your sauce or soup.

Reduction

This is the process of cooking a liquid until some or most of the water has evaporated. This will not only thicken the sauce, but will intensify the flavors, as well. Using a heavy pot bring the liquid or sauce to a simmer and cook until the required consistency is achieved.

Slurry

A slurry is a mixture of starch and cold water or milk.  You can use cornstarch, potato starch, arrowroot, rice flour, or regular flour. Typically 1 part starch to 2 parts liquid. 

Other Common Sauces/Condiments

Mayonnaise - Mayonnaise is an emulsion consisting of oil, egg, salt, vinegar or lemon juice, and egg yolks as an emulsifier.  Many other sauces can be created using this base, with the addition of herbs and seasonings.

Aioli (eye-YO-lee) - (French) The French word for garlic is "ail." Traditional aioli is made by grinding the garlic in a mortar with a pinch of salt, while adding olive oil, a little at a time.  Basically, aioli is garlic-flavored mayonnaise made from pounded cloves of garlic, egg yolks, oil, and lemon juice.  Adding Dijon mustard is a common variation of basic aioli.  If you are fearful of using raw eggs, you can start with mayonnaise, which is made from pasteurized egg yolks. Basic aioli can be seasoned with just about any chopped herbs, spices, or hot pepper sauces.  I love to dip my fries in it.

Coulis (koo-LEE) - A French culinary term. It is a type of a sauce, usually a thick one, which is either entirely or in part from pureed fruits or vegetables. A sauce of cooked down tomatoes can be a tomato coulis, as can a puree of strained blackberries.

Newburg Sauce – This sauce was created at the famous Delmonico Restaurant in New York City by French chef, Charles Ranhofer. This delicious sauce is made with butter, cream, egg yolks, sherry or brandy, paprika and a pinch of cayenne pepper. It is usually served over buttered toast points. If the sauce is used with other foods the dish is given the name “Newburg” such as “Lobster Newburg”.

Remoulade (ray-muh-LAHD) – A chilled flavored mayonnaise used in French cuisine.  It is often aioli or mayonnaise based and may include anchovies or anchovy paste, mustard, capers, horseradish, paprika, curry, chopped pickles, etc.  that are served as a dressing for cold meats, poultry or seafood.