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This monograph contains the advances achieved based on the content ofour previous monograph published in 2011. In other words, the presentmonograph can be considered as "Part II" containing new resultsaccomplished in the last decade. These were published in several reputedinternational journals based on the concept of natural time discussed indetail in our earlier monograph. The analysis in natural time enablesthe study of the dynamical evolution of a complex system and identifieswhen the system enters a critical stage. A wide range of applicationsare discussed, such as the cases of environmental extremeevents-disasters and sudden cardiac death. More light is shed on changesof natural time features before major earthquakes like the 2011 M9Tohoku earthquake in Japan and the 2017 M8.2 Chiapas earthquake inMexico. Hence, natural time analysis plays a key role in predictingimpending catastrophic events in general with a primary audienceResearchers and Academics in Physics, Earth Sciences, and Medicine.