Orbitals: With Applications in Atomic Spectra describes atomic orbitals at a level suitable for undergraduates in chemistry. The mathematical treatment is brought to life by many illustrations rendered from mathematical functions (no artists' impressions), including three-dimensional plots of angular functions, showing orbital phase, and contour plots of the wavefunctions that result from orbital hybridisation. This revised edition includes new discussion of the origins of the colour of gold and the "accidental degeneracy" of the hydrogen atom subshells, a new figure, a new exercise and worked solution, as well as several new references. It also contains current and accurate updates to the old edition. Orbitals extends the key fundamental quantum properties to many-electron atoms, linear combinations of atomic orbitals, simple molecules, delocalised systems and atomic spectroscopy. By focusing on simple model systems, use of analogies and avoiding group theory, results are obtained from initial postulates without the need for sophisticated mathematics. The book explains topics from first principles and guides the reader carefully through the necessary mathematics, supplemented by worked solutions to problems.