Polar oxides surface is intrinsically unstable and thus highly reactive due to the uncompensated surface charges. The charge compensation is accompanied with various surface reconstructions establishing novel functionality for its applications. Thus, a thorough understanding of corresponding surface morphology and atomic configuration at the atomic-scale is indispensable for fully utilizing polar surface. Amongst polar oxides, LaAlO3 stands out as an archetypal polar insulator perovskite, of which (001) surface with single termination, either LaO or AlO2, is polar. Despite extensive efforts have been putted into revealing the termination and reconstruction of LaAlO3 (001) surface, its structural details regarding how the surface terminates still remains ambiguous, in addition, the experimental studies on how the polar surface compensates is also deficient. These are ascribed to the lack of in-situ study of surface evolution under environmental stimulation. Thank for advanced scanning transmission electron microscopy with Cs corrector providing new opportunities on imaging atom dynamic processes. With the newly developed in-situ heating holder accessories, an in-depth discussion about LAO (001) surface characterizations under thermal stimulation becomes possible. In this dissertation, the evolution with temperature and corresponding stabilization mechanisms of LaAlO3 (001) polar surface are discussed with the help from in-situ heating holder and negative spherical aberration (Cs) imaging (NCSI) technique, as well as other STEM techniques.The evolution of LaAlO3 (001) polar surface with temperature was studied systematically. The (LaO)+ terminated LaAlO3 (001) polar surface shows a step-assisted layer-by-layer sublimation at high temperature and tends to be transferred into vicinal surface with (015) orientation after reducing temperature owing to that the step shows repulsion-attraction interactions during annealing. These steps tend to stack together due to the attractive interaction yet be ordered with equal space because of the repulsive interaction. The rest of surface consists of a flat (LaO)+ terminated terrace and a double-LaO-layer surface that is formed by rearrangement of adatoms.A comprehensive study of flat terrace is delivered through an iterative comparison of image simulation and experiment. La vacancy and unexpected O vacancy are detected on the LaO terminated (001) surface, which exists in the form of negatively charged La vacancy and neutral La-O Schottky-like vacancy cluster. The lattice relaxation among several surface layers, showing synergy of vacancies, makes surface thermodynamically stable. The stabilization mechanism of (015) vicinal surface is suggested by investing step structure and electric field. The (015) vicinal surface renders the out-of-plane and in-plane polarization zero totally due to its nonpolar nature and step relaxation. The structure and formation mechanism of double-LaO termination are also discussed, forming a rock-salt unit cell together with the LaO surface layer, which can be compensated by the formation of La vacancies.This dissertation presents careful study of applying advanced scanning transmission electron microscopy to polar oxide surface, which discusses the evolution of LaAlO3 (001) polar surface with temperature using newly developed in-situ heating accessories and suggests the compensation and stabilization mechanisms of the polar surface. We hope that the study not only contributes the polar oxide surface engineering community but also provides guidance for further in-situ (S)TEM research on surface science.