The paper presents the results of investigation of crystal structure, phase content, roughness, and superconducting characteristics of the oxygenated thin films of magnesium diboride (MgB$_{2}$), which are deposited on the dielectric wafers by a magnetron sputtering of the magnesium diboride targets. As demonstrated, the thin films with various degree of perfection of crystal structure and phase composition can be fabricated depending on the parameters of the deposition and annealing processes. Depending on the synthesis conditions, the various types of the vortex pinning can be realized in the films, namely, the pinning at places of fluctuation of the superconducting critical temperature ($\Delta Т_с$-type) and the pinning at the places of fluctuation of the mean free path ($\Delta l$-type). As shown, the deposited thin films consist of the superconducting matrix, which is a solid solution of the oxygen within the magnesium diboride crystal lattice such as MgB$_{x}$О$_{у}$. The density of superconducting critical currents in these films reaches values up to $1,8 \cdot 10^{11}—8,2 \cdot 10^{10}$ А/m$^{2}$ at 10 K and $8 \cdot 10^{10}—2,8 \cdot 10^{10}$ А/m$^{2}$ at 20 K in the fields of 0—1 T (if an external magnetic field is oriented in parallel for the wafer surface).