In modern times, group-theoretical principles have been exploited in the study of atomic and molecular systems, electronic and vibrational spectra of all kinds, a wide variety of thermodynamic systems, chemical reactions, the enumeration of a host of differing chemical species, and the chemical combinatorial problems of many kinds. Chapter 1 of this volume sets out by addressing the meaning of the term "group representation." It explores the various theoretical frameworks that have been evolved for the application of group theory in the physical sciences. Specific applications of combinatorial techniques, derived from or built around the Enumeration Theorem of Polya, in the study of spectroscopy is the theme adopted in chapter 2.;In chapter 3 the spotlight falls on methods that may be used to obtain the eigenvalue spectra of a wide variety of chemically significant molecular graphs while the problem of the treatment of molecular species that do not have a rigid molecular skeleton is addressed in chapter 4. The two final chapters both relate in some way to potential energy surfaces. In chapter 5 the topic under discussion is molecular shape and ways in which this notion may be characterised mathematically. Chapter 6 examines the potential energy surface itself. Here it is shown that group theory can be exploited to minimise the computational effort required to construct the potential energy surfaces and also to ensure that such surfaces correctly simulate dynamically conserved physical quantities.

This volume covers the rapidly developing field of complexity studies. The underlying theme is that complexity is to be found everywhere and the many chemical applications are discussed. The volume offers a comprehensive coverage of complexity and the ways in which it may be measured; complexiy indicies; complexity measures based on Shannon's information theory and thermodynamic complexity. The volume provides a valuable source of reference for graduates and researchers for mathematical chemistry.