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 Readership: Researchers in partial differential equations, mathematical modeling, mathematical physics.