Most of the fractures of engineering structures are due to fatigue and the consequences are disastrous. How to envisage in what operational lifetime fatigue failure would occur, i.e. how to assess the fatigue life, has been one of the most important engineering problems for the last two centuries. There was not any uniform and all-acknowledged solution under any loading including the general multiaxial case of non-proportional, non-cyclic and arbitrary wave-forms of the stress components. According to this book, the lack of solution was for the fatigue life had not been searched for by means of an integral of fatigue damage differentials. A new and radically different IDD approach is proposed: the basic, general notion is loading differential, while loading cycle remains as a particular notion, and the damage differentials per the loading differentials are integrated. Such a possibility had not been revealed and exploited before but it can be practically implemented nowadays thanks to the computers.