Work examines the latest algorithms and tools to solve classical types of diophantine equations.; Unique book---closest competitor, Smart, Cambridge, does not treat index form equations.; Author is a leading researcher in the field of computational algebraic number theory.; The text is illustrated with several tables of various number fields, including their data on power integral bases.; Several interesting properties of number fields are examined.; Some infinite parametric families of fields are also considered as well as the resolution of the corresponding infinite parametric families of diophantine equations.

Preface * Acknowledgements * Introduction * Auxiliary Results, Tools * Auxiliary Equations * Index Form Equations in General * Cubic Fields * Quartic Fields * Quintic Fields * Sextic Fields * Relative Power Integral Bases * Some Higher Degree Fields * Tables * References * Author Index * Subject Index