I have several recipes for aioli and flavored mayo, but none for plain mayonnaise. Mostly because it's more fun to add flavor and you can find a basic mayonnaise recipe anywhere. This is what I used in my cole slaw recipe. I figured if I publish the cole slaw recipe I should include a recipe for mayo on the site for easy reference.
2 cloves garlic, pressed or minced
juice from 1 lemon
1 tsp dry mustard powder
1/2 tsp salt
3/4 cup olive oil
Combine the first 6 ingredients in a food processor. blend thoroughly. slowly drizzle the mayonnaise in while blending. Once all of the olive oil is in, keep blending for a couple more minutes. store in a glass container and refrigerate.