This book represents an advanced theoretical approach to the famous phenomenon of dendritic solidification patterns. The corresponding physical basics are explained and the applied method is introduced in detail. Most of the calculations are carried out explicitly and the elaborate analytical and numerical appendices promote a deep understanding. In contrast to the classical method, no Green's function techniques are required. This enables the consideration of additional nonlinear effects such as convection. Among other things, the selection problem of dendritic growth with anisotropic diffusion is solved. The presented results constitute a remarkable progress in the field of solidification theories.