This monograph is devoted to recent mathematical theories on the bottom up self-organization observed in closed and isolated thermo-dynamical systems. Its main features include: New mathematical results observed in nonlinear systems significantly associated with the physical background on self-organization Mathematically self-contained descriptions based on systematic and comprehensive descriptions of recently developed mathematical techniques Fusion of many areas by strongly supported theoretical leaderships, including, chemotaxis, turbulence, fluid motion, reaction, and network.