Dark matter, though suggested by many astronomical observations, remain a big mystery in modern science. Simulations that assume dark matter particles are heavy and non-self-interacting lead to excessively dense dark matter halos. However, if dark matter particles are repulsively self-interacting or much lighter, the density of dark matter halos could be significantly lower. Therefore, studying the structure of dark matter halos provides an effective way to constrain the nature of dark matter particles. In this talk, I will first introduce the catalogue of 2100 dark matter halos I built for 175 rotationally supported galaxies considering different halo models. This is the largest halo catalogue to date and it has been extensively compared with simulations. With this homogeneous sample, I established the constant volume halo density and provided a direct measurement of halo abundance for the first time. I will then discuss the effect of the interplay between baryons and dark matter, which can dramatically compress dark matter halos for massive galaxies. As such, I invented an innovative approach to derive dark matter halos from observations, which incorporates halo contraction and guarantees dynamical equilibrium. The new approach leads to the discovery of super cusp dark matter halos. In light of this discovery, I will discuss how extending dynamical studies to galaxy clusters can help disentangle the nature of dark matter from baryonic physics, and search for universal scaling relations. I will introduce three approaches to measure cluster mass profiles, including my newly developed approach, i.e. employing cluster galaxies as dynamical tracers. Lastly, I will outline my plan to use dynamical studies of high-redshift galaxies to trace the evolution of dark matter halos and distinguish dark matter from the law of gravity.
