Abstraction is a powerful technique that has not been considered much for nonmonotonic reasoning formalisms including Answer Set Programming (ASP), apart from related simplification methods. We introduce a notion for abstracting from the domain of an ASP program that shrinks the domain size and over-approximates the set of answer sets, as well as an abstraction-&-refinement methodology that, starting from an initial abstraction, automatically yields an abstraction with an associated answer set matching an answer set of the original program if one exists. Experiments reveal the potential of the approach, by its ability to focus on the program parts that cause unsatisfiability and by achieving concrete abstract answer sets that merely reflect relevant details.