Another recipe for Mayonnaise (which seems to differ radically from the one already posted):

Ingredients

3 egg yolks
2 tablespoons vinegar
1/2 teaspoon salt
1/8 teaspoon white pepper
1 1/2 cups oil (I like to use Olive Oil)
Juice of 1/2 small lemon
1 tablsepoon boiling water

Instructions

1. Make sure all ingredients are at room temperature, cold ingredients can cause the mayonnaise to curdle. Beat yolks together with a wire whisk, add vinegar, salt and pepper.
2. Add oil *slowly*, first in drops then in a fine stream. After each 1/2 cup, stop adding oil and beat together mixture.
3. After all oil has been added, stir in lemon juice, then water. Makes about 1 pint.

Variations:

1. Andalouse: peel the skins from 1/4 of one green and one red bell pepper. Cut into julienne strips. Saute in olive oil and cool. Add pepper pieces and 2 tablespoons tomato paste to one cup Mayonnaise, add 1/4 teaspon sugar, 1 mashed gartlic clove and a dash of salt.

2. Chantilly: add 1 tablespoon creme fraiche and one tablespoon lemon juice to 1 cup mayonnaise then stir in 4 tablespoons of whipped cream. For asparagus.

3. Remoulade: Add sieved egg yolks, 1 tablespoon minced sweet pickles, 1/4 teaspoon dry mustard, 1 teaspoon minced parsley, 1/2 teaspoon anchovy paste, 1/2 teaspooon washed capers, 1/2 teaspoon drived cherval and 1/2 teaspoon dried tarragon to 1 cup of Mayonnaise. For seafood.

4. Noisette: Add 1/2 cup toasted ground hazelnuts to 1 cup mayonnaise. For green vegetables.