You can liberally eat nutrient-rich unprocessed foods like animal flesh (meat, fish and poultry). You can have red meat, fish (including shellfish), fowl, and regular cheese (not "diet" cheese, cheese spreads, or whey cheeses). You can also cook with butter, have mayo with your tuna, and add olive oil on your salads.
Then again, carbs are restricted (about 20 grams of net carbs per day, meaning total carbs minus fiber) in the first two weeks. That translates to three cups of loosely packed salad or two cups of salad with two-thirds cup of certain cooked vegetables each day.

The Atkins’ diet menu does allow for adding fruits, vegetables, and whole-grain foods after the two-week induction period