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This thesis documents the first realization of a nuclear clock, a promising next-generation platform for precision metrology and fundamental physics, based on a 8.4 eV transition in thorium-229. Using a vacuum ultraviolet frequency comb developed by the author, the narrow 229Th nuclear clock transition in a solid-state CaF2 host crystal was studied in high resolution spectroscopy, resulting in quantum state resolution to reveal the underlying nuclear structure and establishment of a direct frequency connection between the nuclear clock and an optical atomic clock. This work marks the start of nuclear-based solid-state optical clocks and demonstrates the first comparison of nuclear and atomic clocks for fundamental physics studies. The thesis represents a remarkable convergence of precision metrology, ultrafast strong-field physics, nuclear physics, and fundamental physics. The key results that comprise this thesis are: the unprecedented precision achieved for the measurement of the narrow nuclear transition (~100 kHz linewidth, ~600 s lifetime, and absolute frequency determination to 12 significant digits); a spectrum of nuclear quadrupole splitting peaks, and the direct determination of the ratio of quadrupole moments between the ground and isomeric states; and the detailed description and characterization of the world's unique high resolution VUV frequency comb.