Aioli is arguably the greatest cold sauce of all time. Yet it's nothing more than olive oil emulsified into freshly crushed garlic, seasoned simply with salt and lemon. This is pure, fiery, intense garlic flavor like you may have never tasted.
Aioli is best eaten fresh, but should be okay for about 24 hours.
Since this sauce has such a sharp, hot flavor from the garlic, you don't want to use a really strongly flavored olive oil. We don't want anything too peppery and bitter, which will clash with the garlic. Use something on the mild side, or cut with a neutral vegetable oil.