In our books and scientific reports we have presented some results of the work we have done in the theory of classical Cellular Automata (CA) and their appendices during 1969–2013, in truth with considerable pauses. These results at present form a rather essential constituent of the CA–problematics. In particular, we have studied such problems as the nonconstructability problem, decomposition of global transition functions, extremal constructive opportunities, the complexity of finite configurations and global transition functions, the modelling problem in the classical CA, computer simulation of CA, certain applied aspects of CA, etc. The contents of our last book in context of its chapters can be presented as follows: Introduction Chapter 1. The basic concept of homogeneous structures (HS–models, Cellular Automata) Chapter 2. Nonconstructability problem in classical homogeneous structures (Cellular Automata) Chapter 3. Extremal constructive opportunities of the classical homogeneous structures Chapter 4. Problem of complexity of finite configurations in classical homogeneous structures Chapter 5. Parallel formal grammars and languages defined by homogeneous structures Chapter 6. The modelling problem in the classical homogeneous structures along with certain related questions Chapter 7. The decomposition problem of global transition functions in classical homogeneous structures Chapter 8. Certain applied aspects of the HS–problematics Conclusion