A new experimental limit on the electric-dipole moment (EDM) of the neutron has been established. The experiment, conducted at the Institut Laue-Langevin (ILL), Grenoble, used ultracold neutrons (UCNs) stored in a trap with uniform electric and magnetic fields. A cohabiting atomic-mercury magnetometer was used to reduce spurious signals from magnetic-field fluctuations. Systematic uncertainties, including geometric-phase-induced false EDMs, were carefully studied. Two independent analyses were performed, leading to an upper limit of |d_n| < 2.9 × 10⁻²⁶ e cm (90% CL) for the absolute value of the neutron EDM. The EDM measurement technique involved ultracold neutrons stored in a trap with uniform E and B fields. The Larmor frequency of the neutron spin polarization precession was measured using the Ramsey separated oscillatory field magnetic resonance method. The transition frequency was measured by observing the precession of the neutron spin in a magnetic field. The EDM was determined by analyzing the shift in the transition frequency as the electric field alternated between being parallel and antiparallel to the magnetic field. The experiment involved a detailed analysis of systematic errors, including geometric-phase effects, which were found to contribute to the measured EDM. The geometric-phase effect from the mercury atoms was found to be 50 times larger than that from the UCNs. The analysis also considered other systematic errors, such as light shifts, direct light shifts, uncompensated magnetic field fluctuations, electric forces, leakage currents, and AC ripple. These effects were found to contribute small systematic uncertainties to the EDM measurement. The results from two different analyses were consistent, with the first analysis yielding a value of d_n = (-0.2 ± 1.6 (stat)) × 10⁻²⁶ e cm and the second analysis yielding d_n = (+0.2 ± 1.5 (stat) ± 0.7 (syst)) × 10⁻²⁶ e cm. Both analyses led to an upper limit of |d_n| < 2.9 × 10⁻²⁶ e cm (90% CL) for the absolute value of the neutron EDM. This result represents an improved experimental limit on the neutron EDM, providing tighter constraints on theories that attempt to explain CP violation.A new experimental limit on the electric-dipole moment (EDM) of the neutron has been established. The experiment, conducted at the Institut Laue-Langevin (ILL), Grenoble, used ultracold neutrons (UCNs) stored in a trap with uniform electric and magnetic fields. A cohabiting atomic-mercury magnetometer was used to reduce spurious signals from magnetic-field fluctuations. Systematic uncertainties, including geometric-phase-induced false EDMs, were carefully studied. Two independent analyses were performed, leading to an upper limit of |d_n| < 2.9 × 10⁻²⁶ e cm (90% CL) for the absolute value of the neutron EDM. The EDM measurement technique involved ultracold neutrons stored in a trap with uniform E and B fields. The Larmor frequency of the neutron spin polarization precession was measured using the Ramsey separated oscillatory field magnetic resonance method. The transition frequency was measured by observing the precession of the neutron spin in a magnetic field. The EDM was determined by analyzing the shift in the transition frequency as the electric field alternated between being parallel and antiparallel to the magnetic field. The experiment involved a detailed analysis of systematic errors, including geometric-phase effects, which were found to contribute to the measured EDM. The geometric-phase effect from the mercury atoms was found to be 50 times larger than that from the UCNs. The analysis also considered other systematic errors, such as light shifts, direct light shifts, uncompensated magnetic field fluctuations, electric forces, leakage currents, and AC ripple. These effects were found to contribute small systematic uncertainties to the EDM measurement. The results from two different analyses were consistent, with the first analysis yielding a value of d_n = (-0.2 ± 1.6 (stat)) × 10⁻²⁶ e cm and the second analysis yielding d_n = (+0.2 ± 1.5 (stat) ± 0.7 (syst)) × 10⁻²⁶ e cm. Both analyses led to an upper limit of |d_n| < 2.9 × 10⁻²⁶ e cm (90% CL) for the absolute value of the neutron EDM. This result represents an improved experimental limit on the neutron EDM, providing tighter constraints on theories that attempt to explain CP violation.