This text explores using game theory in mathematical modelling. It is an introductory text, covering the basic ideas and methods of game theory as well as the necessary ideas from the vast spectrum of scientific study where the methods are applied. It has by now become generally apparent that game theory is for many a fascinating branch of mathematics, with both serious and recreational applications. Strategic behaviour arises whenever the outcome of an individual's action depends on actions to be taken by other individuals - whether human, as in the Prisoners' Dilemma, or otherwise, as in the duels of damselflies. As a result, game-theoretic mathematical models are applicable in both the social and natural sciences.