The stars within 25 pc constitute the sample that we aspire to know thoroughly. A well-understood, volume-limited sample of nearby stars is an essential input for the stellar luminosity function, the mass-luminosity relationship, the stellar velocity distribution, and the stellar multiplicity fraction, including substellar companions. Such samples help define stellar populations and estimate the amount mass contributed by local stars. In addition, the stars in this volume provide insight into stellar evolution and the history of star formation in the disk. These physical relationships and subsamples describe the makeup of our Galaxy and, by extension, more distant galaxies (Kuiper 1942; Reid & Cruz 2002). However, models are being developed from an incomplete catalog with limited parameters. Although trigonometric parallaxes establish both sample membership and the cosmic distance scale, many objects within reach of ground-based telescopes remain unmeasured. To advance the solar neighborhood census, observations of 56 nearby stars are presented, including astrometric companion search results, along with a possible a new infrared parallax program. Among these nearby stars, Barnard’s star is a fascinating M dwarf, not only because of its nearness and high proper motion, but also because of van de Kamp’s (1963) announcement that it had a planet. However, PDS scans and analyses of 900 Leander McCormick Observatory photographic plates failed to detect any planets. This time-series analysis using Lomb-Scargle periodograms (Press et al. 1996) would have detected planets with 2.2 Jupiter masses (MJ) or greater. Prior to the timeseries analysis, the relative parallax, proper motion, and secular acceleration of Barnard’s star were measured to be 546 1 mas, 10.3612 0.0002 yr 1 in 355.905 0.001 , and 1.25 0.04 mas yr , respectively. The available photometry and spectroscopy of the 12 reference stars used indicate a correction to absolute of 6 7 mas would be necessary, resulting in an absolute parallax of 552 7 mas, corresponding to a distance of 1.81 0.02 pc and a transverse velocity of 89 km s . These results are comparable to those obtained with more modern equipment. An additional search for potential nearby planets was undertaken through similar time-series analyses of stars in the University of Virginia Southern Parallax Program (SPP; Ianna 1993). For 12 stars (LHS 34, 271, 337, 532, 1134, 1565, 2310, 2739, 2813, 3064, 3242, and 3418), no indication of any unseen companions was detected. However, LHS 288 shows trends suggestive of a 2.4MJ planet in a 7 yr orbit. These high proper motion stars all lie within the solar neighborhood. With the exception of the white dwarf LHS 34, these stars are M dwarfs. After a minimum of 50 observations spread over at least 3 years, the relative parallax solutions have errors of less than 3 mas. An upper limit to the mass of companions remaining undetected was established for each star individually; for longperiod orbits, these range from 1.7MJ to 18MJ. The lack of any clear signal due to a companion may suggest that gas giants are less common around M dwarfs than solar-type stars. Before astrometric companions are investigated, trigonometric parallaxes are obtained that can establish membership in the solar neighborhood. A subsample of 43 potential nearby stars was included in the Cerro Tololo Inter-American Observatory Parallax Investigation (CTIOPI), based on less accurate photometric and spectroscopic distance estimates. Astrometric, photometric, and spectroscopic observations began in 2003 December. Although at least another year of observations is anticipated to finalize these measurements, preliminary results based on observations through mid-2006 are available. According to preliminary parallaxes from this CTIOPI subsample, 28 of the stars are probable members of the solar neighborhood, including three stars (LP 991-84, LHS 6167, and LP 876-10) that apparently lie within 10 pc. Three more stars lie near the 25 pc boundary, and their final parallaxes may still qualify them as members. In addition, LP 869-26 is an apparent binary with newly resolved components separated by approximately 0.7 0.3 . The nearest stars tend to display large proper motions. As expected, high proper motion stars predominate in this subsample. Preliminary proper motions indicate that nine stars have proper motions greater than 0.5 yr , with 2MASS 02511490 0352459 and 23062928 0502285 moving more than 1.0 yr . For this subsample, the proper motions convert to tangential velocities that range from about 10 to 129 km s . Previously unidentified members of the solar neighborhood are anticipated to be so cool, red, and dim that they were missed in previous studies. Preliminary photometry (VC, RC, and IC) is available for 16 stars in this CTIOPI subsample. These stars range from approximately 10th to 20th magnitude in VC. In