A search forνµ →νe oscillations has been conducted at the Los Alamos Meson Physics Facility by usingνµ from µ + decay at rest. Theνe are detected via the reactionνe p → e + n, correlated with a γ from np → dγ (2.2 MeV). The use of tight cuts to identify e + events with correlated γ rays yields 22 events with e + energy between 36 and 60 MeV and only 4.6 ± 0.6 background events. A fit to the e + events between 20 and 60 MeV yields a total excess of 51.8 +18.7 −16.9 ± 8.0 events. If attributed toνµ →νe oscillations, this corresponds to an oscillation probability of (0.31 +0.11 −0.10 ± 0.05)%. 14.60. Pq, 13.15.+g We present the results from a search for neutrino oscillations using the Liquid Scintillator Neutrino Detector (LSND) apparatus described in reference [1]. The existence of neutrino oscillations would imply that neutrinos have mass and that there is mixing among the different flavors of neutrinos. Candidate events in a search for the transformationν µ →ν e from neutrino oscillations with the LSND detector have previously been reported [2] for data taken in 1993 and 1994. Data taken in 1995 have been included in this paper, and the analysis has been made more efficient.Protons are accelerated by the LAMPF linac to 800 MeV kinetic energy and pass through a series of targets, culminating with the A6 beam stop. The primary neutrino flux comes from π + produced in a 30-cm-long water target in the A6 beam stop [1]. The total charge delivered to the beam stop while the detector recorded data was 1787 C in 1993, 5904 C in 1994, and 7081 C in 1995. Most of the π + come to rest and decay through the sequence π + → µ + ν µ , followed by µ + → e + ν eνµ , supplyingν µ with a maximum energy of 52.8 MeV. The energy dependence of theν µ flux from decay at rest (DAR) is very well known, and the absolute value is known to 7% [1,3]. The open space around the target is short compared to the pion decay length, so only 3% of the π + decay in flight (DIF). A much smaller fraction (approximately 0.001%) of the muons DIF, due to the difference in lifetimes and that a π + must first DIF. The totalν µ flux averaged over the detector volume, including contributions from upstream targets and all elements of the beam stop, was 7.6 × 10 −10ν µ /cm 2 /proton. Aν e component in the beam comes from the symmetrical decay chain starting with a π − . This background is suppressed by three factors in this experiment. First, π + production is about eight times the π − production in the beam stop. Second, 95% of π − will come to rest and are absorbed before decay in the beam stop. Third, 88% of µ − from π − DIF are captured from atomic orbit, a process which does not give aν e . Thus, the relative yield, compared to the positive channel, is estimated to be ∼ (1/8) × 0.05 × 0.12 = 7.5 × 10 −4 . A detailed Monte Carlo simulation [3], gives a value of 7.8 × 10 −4 for the flux ratio ofν e toν µ .The detector is a tank filled with 167 metric tons of dilute liquid scintillator, located about 30 m from the neutrino source, and surrounded on all s...