This paper presents a novel approach for real-time visual-inertial odometry (VIO) by preintegrating inertial measurements between keyframes into single relative motion constraints. The key contributions are: (1) a preintegration theory that properly addresses the manifold structure of the rotation group SO(3), enabling the computation of all necessary Jacobians for optimization and a-posteriori bias correction in analytic form; and (2) the integration of the preintegrated IMU model into a visual-inertial pipeline under the unifying framework of factor graphs, allowing the use of a structureless model for visual measurements and accelerating computation. The method is evaluated on real and simulated datasets, demonstrating accurate real-time state estimation outperforming state-of-the-art approaches. The paper also provides a tutorial on uncertainty representation on manifolds and uncertainty propagation. The proposed approach is implemented in the GTSAM 4.0 optimization toolbox.This paper presents a novel approach for real-time visual-inertial odometry (VIO) by preintegrating inertial measurements between keyframes into single relative motion constraints. The key contributions are: (1) a preintegration theory that properly addresses the manifold structure of the rotation group SO(3), enabling the computation of all necessary Jacobians for optimization and a-posteriori bias correction in analytic form; and (2) the integration of the preintegrated IMU model into a visual-inertial pipeline under the unifying framework of factor graphs, allowing the use of a structureless model for visual measurements and accelerating computation. The method is evaluated on real and simulated datasets, demonstrating accurate real-time state estimation outperforming state-of-the-art approaches. The paper also provides a tutorial on uncertainty representation on manifolds and uncertainty propagation. The proposed approach is implemented in the GTSAM 4.0 optimization toolbox.