Peter C. Li and Pierre A. Humblet. / Caption title. / Includes bibliographical references (p. 1). / Supported by the NSF. 9206379-NCR

In this thesis, we present the spectral and timing variabilities of anomalous X-ray pulsar 1E 2259+586 observed with European Photon Imaging PN Camera (EPIC PN) on board X-ray Multi Mirror Mission (XMM), Proportional Counter Array (PCA) on board Rossi X-ray Timing Explorer (RXTE) and Advanced CCD Imaging Spectrometer (ACIS) on board Chandra X-ray Observatory. We presented the results of spectral analysis of 2000 January 11 ACIS observation. Pulse phase spectroscopy was performed on two XMM observations before and after the outburst. Pulse profiles of two XMM observations before the outburst and three XMM observations after the outburst were studied. Results are consistent with the those presented by Patel et al. (2001) and Woods et al. (2004). We searched for the spectral variations versus spin rate during the outburst. Long-term spectral, frequency and spin-down rate variations are presented between 1996 and 2006 including 98 RXTE and 4 XMM observations. However, except outburst region (Woods et al. 2004) no significant spectral and spin rate variabilities were seen. Around the outburst region we confirmed the spectral hardening with increasing spin rate and flux.