Heat the oil in a large skillet over medium-high heat. Add the diced eggplant and saute for 5 minutes, or until it begins to brown. Using a slotted spoon, remove the eggplant from the pan and set aside. In the same hot pan add the diced onion and celery; saute until translucent but not browned. Stir in the garlic and saute a minute or two longer. Add the eggplant back into the pan along with the diced tomatoes, vinegar, sugar, tomato paste, capers, olives, salt, and pepper.
Gently stir the ingredients. Bring the mixture to a simmer and cook it for approximately fifteen minutes, stirring frequently. Stir in the minced basil. Taste the caponata, and if necessary adjust the seasoning with more vinegar, sugar, or salt. Serve caponata hot, cold, or at room temperature as a relish/dip or side dish.