This monograph contains the advances achieved based on the content of

our previous monograph published in 2011. In other words, the present

monograph can be considered as "Part II" containing new results

accomplished in the last decade. These were published in several reputed

international journals based on the concept of natural time discussed in

detail in our earlier monograph. The analysis in natural time enables

the study of the dynamical evolution of a complex system and identifieswhen the system enters a critical stage. A wide range of applications

are discussed, such as the cases of environmental extreme

events-disasters and sudden cardiac death. More light is shed on changes

of natural time features before major earthquakes like the 2011 M9

Tohoku earthquake in Japan and the 2017 M8.2 Chiapas earthquake in

Mexico. Hence, natural time analysis plays a key role in predicting

impending catastrophic events in general with a primary audienceResearchers and Academics in Physics, Earth Sciences, and Medicine.