of these phase bin can vary from -1.71 to -2.65. The observations of X-ray emission from the Crab pulsar also indicate that its spectral energy distribution is changing within its double peak pulse profile. Pravdo et al. (1997) analyzed the RXTE data between 5 and 250 keV, and showed an evolution of the spectral index across the X-ray pulse in a reverse S shape. Massaro et al. (2000) presented the phase-resolved analysis results based on BeppoSAX data. Kuiper et al. (2001) have summarized the basic observational properties of the Crab pulsar from soft X-rays to high-energy gamma-rays. Here, we summarize the basic observed properties at X-rays are as follows: (i) a double pulse profile with a bridge separated by $\sim 0.4$ in phase has been observed; (ii) the spectra of the two peaks soften and the softest spectrum is the first peak; (iii) the spectrum the peaks hardens; and (iv) spectral indices are clearly increasing with energy over all the phase interval. The Chandra X-Ray Observatory has also observed the Crab pulsar using the Low-Energy Transmission Grating with the High-Resolution Camera. Time-resolved zeroth-order images reveal the pulsar emits X-rays at all pulse phases (Tennant et al. 2001). A preliminary analysis 