We introduce the modern tendencies of the topics presented in the first volume of this dissertation thesis. The main goal is to prove that P != NP done in the end of this book.The appendix describes the technique of building modern-aware software product like Regex+ Java package.The specific class of impractical or exponential measures of complexity against the polynomial ones is also discussed - for this case we divide these classes according to the discrete numbers which are known to the present time. We also present the approximate algorithm for the classical NP-complete problem like Traveling Salesman using the memory construction. The question of P and NP equality is important in decision-making algorithms which commonly decide inequality of these classes - we define the memory factor which is exponential and space consumption is non-deterministic. The memory consumption problem within the memorization principle or dynamic programming can be of varying nature giving us the decision to build the approximation methods like it's shown on the example of Traveling Salesman problem.