This dissertation addresses two cosmological applications of the Lyman-alpha (Ly ɑ) forest observed in QSO pairs separated by several arcminutes or less. The Ly ɑ flux autocorrelation and cross-correlation provide a measurement of cosmic geometry at z > 2, via a variant of the Alcock-Paczyński test. I present the results of an observing campaign to obtain moderate resolution spectroscopy of the Ly ɑ forest in QSO pairs with small redshift differences (Δz < 0.25) and arcminute separations (θ < 5'). This new sample includes 29 pairs and one triplet suitable for measuring the cross-correlation and 78 individual QSO spectra for determining the autocorrelation. Continuum fits are provided, as are seven revisions for previously published QSO identifications and/or redshifts. Using a suite of hydrodynamic simulations, anisotropies in the Ly ɑ flux correlation function due to redshift-space distortions and spectral smoothing are investigated for 1:8 ≤ z ≤ 3, further enabling future applications of the Alcock-Paczyński test with Ly ɑ correlation measurements. Sources of systematic error including limitations in mass-resolution and simulation volume, prescriptions for galactic outflow, and the observationally uncertain mean flux decrement are considered. The latter is found to be dominant. An approximate solution for obtaining the zero-lag cross-correlation for arbitrary spectral resolution is presented, as is a method for implementing the resulting anisotropy corrections while mitigating systematic uncertainty.