The generation of the advanced bright coherent ultrafast light source from ultraviolet (UV) to soft X-ray have been pursued for decades. It requires the development of light conversion technique, such as high-order harmonics generation (HHG), as well as the driving laser. In this thesis, we first demonstrate the highest pulse energy (10 mJ), single-stage, ultrafast (45 fs) Ti:sapphire amplifier to date, with a repetition rate of 1 kHz. We then use this laser to pump an optical parametric amplifier system and generate 1.3 μm, 30 fs pulses with sufficient energy (2 mJ) for optimally-efficient, phase matched HHG conversion. This allows us to demonstrate the highest flux, soft X-ray HHG source to date with \u3e 106 photons/pulse/1% bandwidth at 1 kHz (corresponding to \u3e 109 photons/s/1% bandwidth) in a broadband, continuum, spectrum extending to 200 eV, through the fully phase matched hollow waveguide geometry HHG. This photon flux represents an approximately 3 orders-of-magnitude increase compared with past work. Meanwhile, due to the experimental similarity, the high energy ultrashort (10 fs) UV source is implemented in parallel to the soft X-ray source by the four wave mixing (FWM) process. The pulse energy (32 uJ) of UV source is increased by more than 3 times compared with past work, with the pulse duration compressible to less than 13 fs. Finally, utilizing the unique bright supercontinuum HHG soft X-ray source, we have demonstrated soft X-ray absorption spectroscopy of multiple elements and transitions in molecules simultaneously, with the ability to resolve near edge fine structure with high fidelity. The Xeon photon-ionization process is also resolved in the EUV transient absorption spectroscopy experiment by tuning the soft X-ray source to the EUV region, which shows the stability, tunability, and applicability of our tabletop extreme nonlinear light source for the time-resolved experiments
