This thesis presents the analysis of high-resolution, low-signal-to-noise spectroscopic observaitons of a kinematically selected group of about 1300 F-, G-, and K-type dwarfs with proper motions larger than 0.26" per year. The sample includes a significant fraction of stars from the halo of our Galaxy, and the main goal is to characterize the population of spectroscopic binaries in the halo and compare these characteristics with those of the binaries in the disk, to investigate possible differences in the processes of binary star formation. The frequency of spectroscopic binaries with periods less than about 2000 days among the extreme Population II stars is found to be at least 20%, and agrees with the value for Population I. Discrepancies with previous studies which indicated a much lower frequency in the halo are investigated. The distribution of mass ratios (q=M2/M1) is determined here for the first time for the metal-poor binaries, and displays significant differences with the distribution for disk stars. While the latter seems to be essentially flat, the distribution for the halo is found to increase steadily towards q=1, suggesting that Population II systems tend to form with nearly equal-mass components. The difference, however, is shown to be due to a significant contribution from remnants of stellar evolution (white dwarfs), which distort the secondary mass distribution in a sample as old as the halo. The excess over the disk distribution is in good agreement with theory, both qualitatively and quantitatively, and evidence is presented that these binaries with probable white dwarf secondaries tend to have longer orbital periods, as expected from mass transfer or mass loss known to occur during the giant and supergiant phase. After accounting for this effect, the mass distribution for the secondary components in the halo is found to be consistent with that in the Galactic disk. The orbital period distribution and the eccentricity distribution are also similar. Thus, four of the fundamental properties of spectroscopic binaries--the distributions of companion masses, periods, eccentricities, and also the frequency--are comparable in the two populations, which argues that the mechanism that forms binaries is the same, independent of initial conditions in the interstellar medium (chemical composition, turbulence, kinematics). This important conclusion may be relevant for the development of theories of binary star formation. There is clear evidence of orbital evolution among the binaries in this sample, shown by tidal circularization of all orbits with periods shorter than a certain value. The transition period in the halo as marked by the longest circular orbit is seen to be at least as long as 19 days which is longer than that of any other sample of coeval binaries. As predicted by recent theories, this is consistent with the halo being much older, and suggests that tidal circulation is effective not only during the pre-main-sequence phase, but also during the hydrogen-burning stage of stellar evolution.