Beat eggs until very thick and lemon colored. Beat in mashed garlic and salt. Beating constantly, add olive oil Very Slowly - literally drop by drop. After about half the oil has been added and the mixture is thickening, add vinegar and lemon juice. Then continue adding olive oil slowly, beating until a thick emulsion is formed.
Aioli may be used as a garlicky alternative to mayonnaise, but is delicious on its own as a sauce or dip for seafood or vegetables.