Abstract: The Hot Universe Baryon Surveyor (HUBS) mission will carry a nested X-ray telescope capable of observing an energy range from 0.5 keV to 2 keV to study hot baryon evolution. In this paper, we report the latest progress in the design and construction of nested X-ray telescopes which were designed to use a three-stage conic-approximation type assembly to simplify the manufacturing process. The mirror substrate is made using the thermal glass slumping method, with mirrors characterized by a root-mean-square roughness of 0.3 nm, with expected high reflectivity and good thermal stability. We also discuss methods of telescope construction and conduct a deformation analysis of the manufactured mirror. The in situ measurement system program is developed to guide the telescope assembly process.