Most of the baryonic matter in the Universe is not locked in stars. Instead, groups and clusters of galaxies as well as early-type galaxies contain a large mass of baryons in X-ray emitting hot gas. The study of such hot gas provides us a better understanding not only about the evolution of hierarchical structure formation and metal enrichment processes but also about baryon physics such as radiative cooling, ram pressure stripping, heating from active galactic nucleus (AGNs) and galactic winds. Moreover, such knowledge is invaluable for us to probe cosmology through galaxy clusters. In this dissertation I investigated the hot gas properties of galaxies and galaxy groups in three major scientific projects: (1) The measured metal abundance of the hot gas in early-type galaxies has been known to be lower than theoretical expectations. This may be related to the dilution of hot gas by mixing with cold gas. We studied the hot gas metal abundance with a sample of 32 early-type galaxies observed by Chandra and XMM-Newton. We find that there is virtually no correlation between hot gas Fe abundances and their atomic gas content. In contrast, we demonstrate a negative correlation between the measured hot gas Fe abundance and the ratio of molecular gas mass to hot gas mass. (2) We studied the X-ray brightest fossil group (poor cluster) ESO~3060170 out to its virial radius with Suzaku. The entropy and pressure profiles in the outer regions are flatter than in simulated clusters, similar to what is seen in observations of massive clusters. This may indicate that the gas is clumpy and/or the gas has been redistributed. (3) The nearby group centered on its bright central galaxy NGC~1407 has been thought to be an unusually dark system from previous kinematic studies. It is also known for hosting a bright galaxy NGC~1400 with a huge radial velocity difference (1200 km s−1) with respect to the group center. We investigated the NGC~1407/1400 complex with XMM-Newton and Chandra observations. We show that a region of enhanced surface brightness between NGC~1407 and NGC~1400 is likely to be hot gas stripped from NGC~1400's ISM. We inferred that NGC~1407 system has a normal mass-to-light ratio from an X-ray--determined hydrostatic mass estimate.