Hollandaise sauce is an emulsion of egg yolk and butter.   Lemon juice, salt, and a little white pepper or cayenne pepper are often added as seasoning.  Hollandaise light yellow and opaque, smooth and creamy: it tastes rich and buttery, with a mild tang added by the seasonings, but not so strong as to overpower mildly flavoured foods.  Hollandaise sauce is well known as a key ingredient of Eggs Benedict, and is often paired with vegetables such as steamed asparagus.

Hollandaise is one of the five mother sauces in French haute cuisine.

History
Hollandaise sauce  got its name because it was thought to be like a Dutch sauce. As early as 1651, François Pierre La Varenne describes a sauce similar to hollandaise sauce in his groundbreaking cookbook Le Cuisinier François:
"avec du bon beurre frais, un peu de vinaigre, sel et muscade, et un jaune d’œuf pour lier la sauce"
("with good fresh butter, a little vinegar, salt, and nutmeg, and an egg yolk to bind the sauce")
.
Alan Davidson notes a "sauce à la hollandoise" from François Marin's Les Dons de Comus (1758), but since that sauce included flour, bouillon, and herbs, and omitted egg yolks, it may not be related to the modern hollandaise.

Mrs. Isabella Beeton's Household Management had recipes in the first edition (1861) for "Dutch sauce, for fish" (p. 405) and its variant on the following page, "Green sauce, or Hollandaise verte". Her directions for hollandaise seem somewhat fearless:
"Put all the ingredients, except the lemon-juice, into a stew-pan; set it over the fire, and keep continually stirring. When it is sufficiently thick, take it off, as it should not boil ..."

Derivatives of hollandaise sauce
Being a mother sauce, hollandaise sauce is the foundation for many others made by adding or changing ingredients. The following is not a complete list of such minor sauces.
The most common derivative is Sauce Béarnaise.  It can be made by replacing the acidifying agent (vinegar reduction or lemon juice) with a strained reduction of vinegar, shallots, fresh chervil, fresh tarragon and crushed peppercorns.  Alternatively, the flavourings may be added to a standard hollandaise. Béarnaise and its children are often used on steak or other "assertive" grilled meats and fish.
Sauce Choron is a variation of béarnaise without tarragon or chervil, plus added tomato purée.
Sauce Foyot (a.k.a. Valois) is béarnaise with meat glaze (Glace de Viande) added.
Sauce Colbert is Sauce Foyot with the addition of reduced white wine.
Sauce Café de Paris is béarnaise with curry powder added.
Sauce Paloise is a version of béarnaise with mint substituted for tarragon.
Sauce au Vin Blanc (for fish) is produced by adding a reduction of white wine and fish stock to hollandaise.
Sauce Bavaroise is hollandaise made with crayfish butter with added cream, crayfish tails horseradish, and thyme.
Sauce Crème Fleurette is hollandaise with crème fraîche added.
Sauce Dijon, also known as Sauce Moutarde or Sauce Girondine, is hollandaise with Dijon mustard.
Sauce Maltaise is hollandaise to which blanched orange zest and the juice of blood orange is added.
Sauce Mousseline, also known as Sauce Chantilly, is produced by folding whipped cream into hollandaise.
If reduced sherry is first folded into the whipped cream, the result is Sauce Divine.
Sauce Noisette is a hollandaise variation made with browned butter (beurre noisette).

Physico-chemical properties 
Like Mayonnaise, hollandaise sauce is an emulsion. Hollandaise sauce is classified as an emulsified butter sauce (beurre blanc).

Unlike sauces thickened with solids, such as starches, emulsions such as Hollandaise sauce are essentially unstable, as it is a liquid-in-liquid solution.

Increasing the viscosity can be done by adding flour or cornstarch and this can also protect against curdling. Curdling occurs when the sauce is cooked too quickly over directly and actually brought to a boil, causing the egg proteins to denature and rearrange or coagulate into curds by bonding to one another. Starches, such as flour and cornstarch, protect against curdling when the starch granules absorb water and being to leak long starch molecules into the liquid. These long starch molecules prevent curdling in two ways. First, they absorb heat and prevent some egg proteins from denaturing. Second, the long dissolved starch molecule get in the way of the egg protein molecules and impede bonding.

Notes

References
 

 

 

 

 
 McGee, Harold (2004). On food and cooking. Scribner. p. 517. .

Other websites
Mrs. Beeton, The book of household Management, 1861: Project Gutenberg e-text
History of Sauces
History of Hollandaise

 How To Make Hollandaise Sauce Step-by-step tutorial from About.com (generally good, but a glass or ceramic bowl is not recommended as they make it too difficult to control the heat)
 Free Culinary School Podcast Episode 8  A podcast (audio) episode that talks about the proper classical technique for making hollandaise and the science behind the method.

Mother sauces
French food