In the book we present some of results of the work we have done in theory of classical Cellular Automata (CA) and their appendices during 1969-2013 in truth with considerable pauses. These results at present form essential constituent of the CA problems. In particular, we have studied such problems as the nonconstructability problem in CA, decomposition of global transition functions in CA, extremal constructive possibilities, complexity of finite configurations and global transition functions, parallel formal grammars along with languages defined by CA, the modelling problem in the classical...