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Following the establishment of quantum mechanics around 80 years ago, many formulae that describe how atoms and molecules interact with each other and with external electromagnetic fields were derived. While such formulae provide prescriptions for calculating atomic and molecular properties many of them are inconvenient to evaluate because of the need to calculate the sums of a, large, often infinite, number of expressions constructed from various matrix elements and excitation energies. Alex Dalgarno through his major work in perturbation theory pioneered the method, now standard, in which these sums are calculated from the solutions of finite numbers of differential equations. This article is a brief summary of the method and its use.