The aim of the study-to demonstrate the properties of the gas-dynamic discontinuity as a singularity the geometry of the Euler equations give on this basis, the definition of the intensity discontinuity. We have considered the gas-dynamic discontinuity conception. We demonstrated geometrical content of gas dynamics equation. The shock-wave process concept (as a transfer function of gas-dynamic variables space reorganization) was introduced. The basic types of gas-dynamic discontinuities: shock waves, compression shocks, centered depression and compression waves, contact discontinuities were considered. The discontinuity intensity concept was introduced. The basic formulae and discontinuity intensity calculation results were given.