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In this paper, a classical theory of inelastic atomic collisions is evolved on the basis of the relations for binary collisions as well as for the Coulomb collisions derived in the laboratory system of coordinates. Built up as an approximation based on the binary collisions, i.e., the independent pair interactions of the individual elements of the colliding systems, the theory, with its immense simplicity, not only permits a clear qualitative interpretation of the atomic collisions, but also describes well their quantitive aspect. In terms of that theory, a majority of basic inelastic processes accompanying the atomic collisions are analyzed. In particular, calculations are made for the following: (i) ionization of atoms and molecules by light particles (electrons), as well as by heavy particles (protons, deuterons), including inner-shell ionization and double ionization; (ii) excitation of single and triplet lines (excitation with exchange and without exchange); (iii) capture of electrons in orbit; (iv) slowing down of heavy charged particles (with consideration of the capture process as well as of the interaction with the Coulomb field of the nucleus); (v) inelastic scattering of electrons on atoms and molecules. According to the theory developed, the "diffraction" of elementary particles on atomic systems is explained on the basis of corpuscular mechanics; it is shown that the discrete energy states of the scatterer electrons---and the anisotropy in the space orientation of their velocities in the case of crystals---are responsible for the main features of the diffraction pattern. Having at our disposal a simple theory without any arbitrary parameters except those describing the target system, we find it a useful tool for the investigation of atomic structures.