Chemistry is a practical subject， so why should mathematics now play such an important role in its understanding？ Coulson provided compelling answers to this question in his presidential address to the Institute of Mathematics and its Applications （Coulson， 1973）， when he reviewed the reactions of those involved in the development of chemical ideas one hundred years earlier. He reminds us， for example， that in 1878 Frankland wrote： 'I am convinced that further progress of chemistry as an exact science depends very much indeed upon the alliance with mathematics'. This prophetic view was not shared by most chemists of the time; and it was not until the development of the quantum theory in the late 1920s， and the consequent impact on our understanding of spectroscopy and electronic structure， that chemists started to develop the mathematical tools that were relevant to the needs of chemistry. There are many reasons for the growth of this symbiotic relationship， and it is helpful to examine some of them in putting the objectives of this book into the proper context.
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