This book is about the importance of random phenomena occurring in nature. Cases are selected in which randomness is most important or crucial, such as Brownian motion, certain reactions in Physical Chemistry and Biology, and intermittency in magnetic field generation by turbulent fluid motion, etc. Due to almighty chance the structures can originate from chaos even in linear problems. This idea is complementary as well as competes with a basic concept of synergetics where structures appear mainly due to the pan-linear nature of phenomena. This book takes a new look at the problem of structure formation in random media, qualitative physical representation of modern conceptions, intermittency, fractals, percolation and many examples from different fields of science.