| Imaging at the nanoscale is of great interest for applications in materials science, nanoscience and biology. The microscopy method developed in this thesis combines a tabletop coherent EUV/X- ray source based on high harmonic generation, and an image-forming method based on coherent diffractive imaging. This microscopy method offers truly diffraction-limited resolution; however, previous work has been limited to thin, isolated samples in transmission mode. This thesis work extends this tool for imaging non-isolated samples, and for working in reflection mode to image surface features of thick samples. The quantitative phase information of the reflection image enables surface profilometry capability with sub-nanometer precision. The microscope developed in this work is also demonstrated to have hyperspectral capability with simultaneous multi-wavelength illumination, without the need for wavelength scanning or energy-resolved detectors. In the future, by taking advantage of the short-pulse nature of the high harmonic illumination, this microscope will be able to image nanoscale ultrafast dynamics with 10 femtosecond temporal resolution, opening the door for imaging at the space-time limits. |