Structure formation in crystallizing polymers, as occurring during processing, has not been treated so far in a coherent form. This fact explains, why this monograph is written as the first book devoted to this subject. A quarter of a century ago the underdevelopment of this subject was obvious. Trial and error dominated. In fact, other apposite subjects as polymer melt rheology or heat transfer, had reached high levels. A great number of books has been devoted to them. Mold filling of amorphous polymers and the solidification of these polymers by vitrification can nowadays be simulated numerically with a high degree of accuracy. In the solidified sample even residual stresses and corresponding birefringence effects can accurately be 1 calculated . However, semicrystalline polymers, which form the majority of industrial po- mers, have been excluded from these considerations for good reasons. In fact, great uncertainties existed about the formation of quality determining crystalline str- tures. In particular, polyolefins suffered from this shortcoming. In 1983 this fact instigated the polymer research group at the Johannes Kepler University in Linz to start with pertinent activities. The urgency of this kind of studies becomes evident, if advantages and hitches of these polymers are considered. 1. Versatility of processing: Injection molding into a great variety of shapes and sizes, from thin walled beakers to garden chairs, not to forget pipe and profile extrusion, cable coating,—ber spinning,—lm blowing. 2. Product qualities: Ductility, low density, good electric insulation, corrosion resistance, surface quality.