| Gamma-ray Astronomy has made significant progress with a series of space and ground-based telescopes and the support of the observations from other wavelength. The field of astrophysical gamma-ray emission has been extremely extended and people can learn more about the astrophysical sources of high-energy gamma rays further. This thesis includes two parts. The first part is the study of the X-ray afterglows of the gamma-ray bursts(GRBs), and the second part is the statistical classification study of the unassociated gamma-ray sources in the Fermi Large Area Telescope (LAT) Catalog.Since the GRBs were discovered in1967, they have been one of the main re-search objects in the Gamma-ray Astronomy. People try to understand the physical nature of the GRBs but until now it still remains a mystery in astrophysics. The shallow decay phase of X-ray afterglows and X-ray flares have been observed by Swift space telescope, both of which are unaccountable in the standard GRBs af-terglow model. These phenomenons give clues to the study of the GRBs center engine. We will try to explain the shallow decay phase of X-ray afterglows in our first part of work. It is widely accepted that this phenomenon indicates a continuous energy injection to the GRBs blastwave and this energy could be released from a fast-rotation megnetar after the GRBs. Based on the knowledge of the evolution of a Poynting outflow, we argue that the injecting flow is an ultra-relativistic and magnetic kinetic-energy flow (i.e., magnetic wind) rather than pure electromagnetic waves or pure wind. The magnetic wind interacting with the GRBs blastwaves will produce the wind termination shock. Our result shows that the emission of the wind termination shock can produce the X-ray afterglows with a shallow decay phase and a normal decay one. The case caused by the wind termination shock supplies a internal dissipation mechanism. A routine whole-sky survey with the Large Area Telescope on board the Fermi Gamma-Ray Space Telescope has been carried out since the year2008. Analyzing the observational results obtained during the first24months, the Fermi LAT Col-laboration had published the Fermi LAT2-Year Source Catalog containing1873gamma-ray sources. They had made great efforts to identify the sources and con-sidered127as being firmly identified and1171as being reliably associated with counterparts of known or likely gamma-ray-producing source classes. So575sources left are unassociated with any counterpart. In our second part of work, we analyze the spatial distribution and the statistic properties of the gamma-ray spectral and variability indices of the remaining575unassociated Fermi LAT sources. As a re-sult, we suggest that, statistically, the Fermi LAT unassociated sources could mainly consist of Galactic supernova remnants/pulsar wind nebulae, BL Lacertae objects, flat spectrum radio quasars, and other types of active galaxies. The corresponding fractions are about25%,29%,41%, and5%, respectively. |