This talk provides an introduction to the fundamentals of simultaneous localization and mapping (SLAM). We aim to provide foundational knowledge, and attendees are not expected to have any prerequisite experience in the field. The talk consists of an introduction to the concept of SLAM, as well as practical design considerations in formulating SLAM problems. Visual inertial odometry will be introduced as a motivating example of SLAM, and we will explain how this problem is structured and solved.