The power of this method was shown by improving the known upper bound, in terms of a graph's order, on the (ordinary) domination number of graphs with minimum degree between 5 and 50. In addition, the reader is exposed to the discharging method of Bujtás. The Continuation Principle is developed, which provides a much-used monotonicity property of the game domination number. Powerful proof methods such as the imagination strategy are presented. A toolbox of proof techniques is provided for the reader to obtain results on the domination game and its variants. The crux of the discussion surrounds new methods and ideas that were developed within the theory, led by the imagination strategy, the Continuation Principle, and the discharging method of Bujtás, to prove results about domination game invariants. This concise monograph present the complete history of the domination game and its variants up to the most recent developments and will stimulate research on closely related topics, establishing a key reference for future developments.
