The reality of a thing is its state of existed, exists, or will exist in the world, independent on the understanding of human beings, which implies that the reality holds on by human beings is local or gradual, and mainly the Mathematical reality, not the reality of a thing. Is our mathematical theory can already be used for understanding the reality of all things in the world? The answer is not because one can not holds on the reality in many fields. For examples, the elementary particle system or ecological system, in which there are no a classical mathematical subfield applicable, i.e., a huge challenge now is appearing in front of modern mathematicians: To establish new mathematics adapting the holds on the reality of things. I research mathematics with reality beginning from 2003 and then published papers on fields, such as those of complex system and network, interaction system, contradictory system, biological populations, non-solvable differential equations, and elementary established an entirely new envelope theory for this objective by flows, i.e., mathematical combinatorics, or mathematics over graphs, which is an appropriated way for understanding the reality of a thing because it is complex, even contradictory. This book collects my mainly papers on mathematics with reality of a thing from 2007 – 2017 and most of them are the plenary or invited reports in international conferences.