Mayonnaise is an emulsion of vegetable oil, egg yolks, lemon juice or vinegar.
Because most mayonnaises are made with soybean oil and contain additives, your best bet is to make your own fresh Homemade Mayonnaise.
But if you're looking for a quick alternative, there are many mayonnaises made from canola or grapessed oil like Vegenaise which is widely available. Better yet, enjoy coconut mayonnaise made by Wilderness Family Naturals.
Widely used as a spread or dressing, mayonnaise is also used as the base for a number of other mixtures aïoli, remoulade, tartar sauce and thousand island dressing.