The book begins with four introductory chapters devoted to Boolean algebraic functions and Binary Decision Diagrams. The rest of the book is based on original results obtained by the author from 1994 to 2014 and reflected, in particular, in English-language conference and journal publications (ISLPD, ICCAD, ED&TC, ISQED, DATE, ACM transactions, etc.), and also in multiple publications in Russian. This manuscript is divided into two parts: Chapters One through Five discuss the theory and applications of decision diagrams, while Chapters Six through Nine concentrate on the theory and applications of logic correlations between circuit signals. Chapter Five contains the results on the BDD of a special type (SP-BDD) and their applications to analysis and optimization of digital CMOS circuits. The second part contains the results on theory and applications of logic correlations between circuit signals (logic implications). The following applications are considered: noise analysis of digital circuits (both functional and delay noise), timing analysis with detecting false paths, and digital circuit obfuscation. Chapter Nine explains the use of TDD (Ternary Decision Diagrams) in digital CMOS simulation with uncertaintyin particular, with power simulationand both with and without accounting for logic implications. The principal audiences for the book are mathematicians and software developers, primarily working in microelectronics CAD.