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...