This article mainly introduced several important inequalities like inequalities and so on in primary,differential and integral these three aspects manifestation,seeks it in the intrinsic structure and the certificate thought organic unification; And produces these inequalities in other aspects some applications.Interrogates mainly lies between the green inequality may accumulate primary form and its the promoted form the integral form which to Riemann,then between integral form relation and proof which may accumulate to Lebesgue . This article mainly introduced several important inequalities like inequalities and so on in primary,differential and integral these three aspects manifestation,seeks it in the intrinsic structure and the certificate thought organic unification; And produces these inequalities in other aspects some applications.Interrogates mainly lies between the green inequality may accumulate primary form and its the promoted form the integral form which to Riemann,then between integral form relation and proof which may accumulate to Lebesgue .