Cellular Neural Networks (CNN's) were introduced in 1988 by L O Chua and L Yang as a novel class of information processing systems, which possesses some of the key features of Neural Networks and which has important potential applications in such areas as image processing and pattern recognition. Many complex computational problems can be formulated, as well-defined tasks where the signal values are placed on a regular geometric 2-D or 3-D grid, and the direct interaction between signal values are limited within a finite local neighbourhood. CNN is an analogue dynamic processor array, which reflects just this property: the processing elements interact directly within a finite local neighbourhood. The purpose of the book is to present the recent results in the basic concepts of dynamics, stability analysis and CNN models of some partial differential equations.