The domination problem in graph theory is to find a minimum sized vertex subset in a graph such that every vertex not in this set is adjacent to at least one vertex in this set. The domination problem and its variations serve as good models for many real problems including location problems in operations research. This comprehensive volume introduces domination and its variations in graphs from an algorithmic point of view. It examines the structures of various graph classes, including trees, chordal graphs, strongly chordal graphs, interval graphs, comparability graphs, permutation graphs, distance-hereditary graphs and generalizations of these graphs. These structure properties provide concepts for designing the algorithms. This useful reference text benefits researchers, academics, and graduate students in theoretical computer science, combinatorics, and operations research.