The study of black holes is one of the most important topics in high energy astrophysics. Cygnus X-1 is one of the most well-studied stellar mass black hole systems. In Cygnus X-1, a black hole is thought to accrete material from the stellar wind of the companion star, HDE 226868. During the process the infalling matter releases enormous amounts of gravitational potential energy, and the material is heated to millions of degrees due to viscous stress. The region around the black hole then emits X-rays. Many X-ray observatories have observed Cygnus X-1, but the details of the environment of Cygnus X-1, including the physical condition of the stellar wind, are still not fully understood. High resolution spectroscopy is a valuable tool for use in such a study. After the launch of the Chandra X-ray observatory, high resolution spectral data have become available. The presence of numerous absorption lines that are associated with highly ionized materials has been revealed by Chandra. The absorption lines provided insight into the details of stellar wind geometry. However, a systematic study of the variability of the absorption lines has not been carried out.;This work addresses the issue in the case of Cygnus X-1. During the study, the dramatic variability of the absorption lines on a time scale of hours was discovered for the first time. The study was based on observation carried out under a program of own. The light curve shows that Cygnus X-1 was brighter during the first half of the observation, so we divided the whole observation into "high" and "low" periods with each period having about a half of exposure time. In the first period of the observation, we detected absorption lines associated with highly ionized Ne, Na, Mg, Al, Si, S, and Fe, some of which had been seen in earlier Chandra observations. Surprisingly, however, most of the lines became undetectable in the second period. The lines weakened by more than two orders of magnitude even though the continuum varied only by 20--30%. The absorption lines are generally attributed to the absorption of X-rays by the ionized stellar wind from the companion star in the binary system. Since the overall X-ray luminosity varied only mildly, the observed variability probably arose from a sudden change in the density of the wind.;To gain deeper insights into the origin of highly variable absorption lines, we examined all archival high resolution spectroscopic observations of Cygnus X-1 that were carried out with Chandra. Similar variable absorption lines were detected in one of the archival observations, so the phenomenon does not seem to be rare. We also looked into plausible dependencies of the lines on the binary orbital motion as well as on the spectral states. Although we saw evidence for such dependencies, the sporadic coverage of the orbit and spectral states makes it difficult to disentangle the two effects. Improved temporal coverage would be needed to make further progress. The study of variabilies of the absorption lines may give further details on the understand of stellar wind and Cygnus X-1 binary system. The results may also be applicable to other black hole systems.;In addition to the main topics of this thesis, two more projects were carried out. In the first project, we searched systematically for X-ray counterparts to some of the unidentified TeV gamma--ray sources near known pulsars, taking advantage of Chandra's unprecedented spatial resolution. The results show that some of the sources are likely pulsar wind nebulae (PWNe). In the second project, the 1Ms Chandra observations of Cassiopeia A were analyzed to take a deep look at the non-thermal filaments near the forward shock. The preliminary results show an interesting trend: the X-ray spectrum of the filaments steepens going outward. Further investigation is on going. Our collaborators are now carrying out detailed modeling of the diffusion, radiation, and advection processes.
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