Accompanied with humanity into the 21st century, a highlight trend for developing a science is its overlap and hybrid, and harmoniously with other sciences, which enables one to handle complex systems in the WORLD. This is also for developing mathematics. As a powerful tool for dealing with relations among objectives, combinatorics, including combinatorial theory and graph theory mushroomed in last century. Its related with algebra, probability theory and geometry has made it to an important subject in mathematics and interesting results emerged in large number without metrics. Today, the time is come for applying combinatorial technique to other mathematics and other sciences besides just to find combinatorial behavior for objectives. That is the motivation of this book, i.e., to survey mathematics and fields by combinatorial principle.