This project is aimed to solving one of the fundamental problems of solid state physics associated with the formation and kinetics of domain structure during switching polarization in ferroelectrics. The aim of the project is to reveal the main regularities of the domain structure kinetics during local polarization switching in thin films of lithium niobate. In this work, the features of the initial domain structure of lithium niobate thin films and the laws of the domain structure kinetics during local spolarization switching will be revealed, and features of the morphology of lithium niobate thin films with different texture and synthesis conditions will also be established. Features of the kinetics of the domain structure for films with different texture and synthesis conditions will be revealed. In addition, the processes of relaxation of the domain structure after local switching over a wide temperature range will be investigated. The results obtained in the course of this scientific research will substantially expand the current understanding of the domain structure evolution in ferroelectric thin films. The results obtained can find application in the development of data storage devices and computing devices based on thin films.