With our fundamental approaches outlined in Chap.  1 , we pay more detailed attention to our technical methods to be used in the following chapters. First, we willWill give the axioms for a toposTopos to be a temporal topos. Then basic concepts from temporal toposTemporal topos, t-topos will be introduced for the applications in Chap.  3 on physics, Chap.  4 on cognitiveCognitive and biological sciences, and Chap.  5 on philosophyPhilosophy, philosophies. Namely, the purpose of this chapter is preparation for the chapters that follow.