"In this thesis I develop a new ⁴⁰Ar/³⁹Ar dating technique for measuring ages and estimating cooling histories of potassium-bearing minerals within shales and clays. To overcome problems of argon recoil, small shale or clay flakes (possessing diameters less than 2 mm) were encapsulated within micro ampoules under vacuum. Encapsulation ensures that argon that recoils from tiny crystals during irradiation in a nuclear reactor cannot escape and will therefore be detected during ⁴⁰Ar/³⁹Ar laser step-heating. The step heating method is effective in differentiating between, and dating neoformed and detrital illite components. My use of this method has revealed a significant age difference across the Toyuk thrust, Brooks Range, northern Alaska. Devonian shales from south of the thrust yield relatively flat age spectra indicative of a younger illitic component, and argon retention ages around 225 Ma. Shale samples from north of the thrust yield staircase age spectra indicative of a detrital illite component, and older retention ages (233-391 Ma). Modeling of these spectra across the Toyuk also suggests that argon loss and subsequent cooling occurred at about 140 Ma. Retention ages across the Toyuk thrust may reflect differences in depths of tectonic burial, or differing ages of crystallization of neoformed illite during initial deposition and burial. ⁴⁰Ar/³⁹Ar age spectra from the Colville basin, North Slope, Alaska, illites are generally dominated by detrital illite, yielding high temperature step-heat ages up to 475 Ma. Illite crystallization ages from the NPRA (National Petroleum Reserve in Alaska) range between 205 and 225 Ma. These ages are older than depositional ages and therefore suggest that this illite was transported from outside the Colville basin, perhaps from the Brooks Range. The Colville basin samples also reveal argon loss at -45 Ma. Paleocene samples from the Exxon Alaska State A-1 well yield illite crystallization ages of about 205 Ma, and argon loss ages around 40 Ma. X -ray diffraction of the Colville basin samples indicates the presence of multiple clay phases, including detrital and neoformed illite. This complex mineralogy precluded estimating when the host shales were within the oil generation window"--Leaves iii-iv.