Generalized and hybrid set can be created with neutrosophy and quad-stage method. Firstly the generalized and hybrid neutrosophic set is discussed. Secondly the combination or synthetical body of generalized and hybrid sets is named as “library” (various generalized and hybrid sets can be put into the related “library”); such as “mathematics library”, “physics library”, and the like. As for the constitution of “library”, the concept and methodology of a special “Four-library” are proposed. Neutrosophy and quad-stage method can also be used to solve many actual problems within the framework of “set” and “library”; for example, based on the analyses of one “Four-library”, jointly solving problem of advance of planet's perihelion with partial results of law of gravity and general relativity; and jointly expanding “uncertainty principle” to “certainty-uncertainty principle set”. Finally, we introduce the concepts of “variational principle of set” and “variational principle of library”, and establish a kind of “partial and temporary unified theory of mathematics so far”.