In this book, we explore the need to understand the process of technological development and its impact on humanity. This text is intended to provide a comprehensive overview of the metrical theory of regular continued fractions and related representations of real numbers. The book has been in the making for a long time, allowing us to refine and improve many parts of it. Despite the differences in style and approach between the two authors, we have made every effort to present a unified and coherent work. The plot of the book 'Metrical Theory of Continued Fractions' revolves around the concept of understanding the process of technological evolution and its impact on humanity. The book explores the need for a personal paradigm for perceiving the technological process of developing modern knowledge as the basis for the survival of humanity and the survival of the unification of people in a warring state. The book begins by defining the regular continued fraction transformation T, which is represented as Tn = alwn + gtoo, where alw is the integer part of 1/w and gtoo is the regular continued fraction expansion of w with respect to Xi1i n. The authors explain that this equation can be written as lim[alw anw] = wE0n, highlighting the name of T.

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