The paper introduces iSAM (Incremental Smoothing and Mapping), a novel approach to the simultaneous localization and mapping (SLAM) problem. iSAM is based on fast incremental matrix factorization, providing an efficient and exact solution by updating a QR factorization of the sparse smoothing information matrix. The method avoids unnecessary fill-in in the factor matrix by periodic variable reordering, making it suitable for robot trajectories with many loops. iSAM also includes efficient algorithms for accessing estimation uncertainties, enabling real-time data association. The paper evaluates iSAM using various simulated and real-world datasets, demonstrating its effectiveness in both landmark-based and pose-only settings. Key contributions include the incremental update of the square root information matrix, periodic variable reordering to prevent fill-in, and efficient algorithms for retrieving estimation uncertainties. The results show that iSAM provides an efficient and exact solution, maintaining sparsity even in large-scale environments with loops.The paper introduces iSAM (Incremental Smoothing and Mapping), a novel approach to the simultaneous localization and mapping (SLAM) problem. iSAM is based on fast incremental matrix factorization, providing an efficient and exact solution by updating a QR factorization of the sparse smoothing information matrix. The method avoids unnecessary fill-in in the factor matrix by periodic variable reordering, making it suitable for robot trajectories with many loops. iSAM also includes efficient algorithms for accessing estimation uncertainties, enabling real-time data association. The paper evaluates iSAM using various simulated and real-world datasets, demonstrating its effectiveness in both landmark-based and pose-only settings. Key contributions include the incremental update of the square root information matrix, periodic variable reordering to prevent fill-in, and efficient algorithms for retrieving estimation uncertainties. The results show that iSAM provides an efficient and exact solution, maintaining sparsity even in large-scale environments with loops.