This book presents the new methodology of science and mathematics, Qualitative Mathematics and Modeling (QMAM) that, together with the introduction of the concept of nested generalized physical fractal, was the crucial factor for the discovery of the superstring, fundamental building block of matter complete with structure and properties, 1997, and the foundation of the Grand Unified Theory (GUT) consolidated from a series of papers in 2008. Qualitative mathematics resolved the 360-year-old Fermat’s last theorem (FLT), 1998, proved the 250-year-old Goldbach’s conjecture, 2003, and developed the new real number system and complex vector plane, 2009, that provide the main mathematics of GUT. The principal theoretical applications of GUT through QMAM are the Unified Theory of Evolution, 2009, Theory of Intelligence, 2012, and theory of chaos and turbulence, 2013. Their practical applications are the design of research and development program on GUT technologies, program of creative mathematics-science education from primary through graduate school and strategy for sustainable development of the Third World. There are definitive statements on the Higgs boson, big bang and “missing link”.