This book describes in mathematical terms the extraction of useful information from ESR spectra as applied to paramagnetic organic, inorganic and organometalic molecules. It lays a firm groundwork for understanding more sophisticated experiments, which the availability of newer commercial instruments has made possible. It takes the reader step by step through obtaining and interpretating ESR spectra of paramagnetic molecules. The mathematical basis of each observed phenomena are detailed and examples given. In particular there is a detailed discussion of 2nd order pertubation theory treatment of the Spin Hamiltonian for non-coincident G and A axes.