Simulataneous Localization and Mapping (SLAM) and path planning are two of the main challenges of autonomous navigation. In the context of driverless racing in Formula Student, those two components have a big impact on the overall performance of the car. In this thesis, we derive how real-time operation, centimeter-precision, low latency and lightweight design of the SLAM system all contribute to maximizing scores. Then, we design and implement SLAM according to those criteria for integration into the GreenTeam E0711-13 race car. State-of-the-art approaches such as factor graphs are used to optimally process the information from perception pipelines as well as other sensors. The system is able to fuse the data from Light Detection and Ranging (LiDAR) and camera to achieve both accurate classification and position estimation of landmarks. The generated map and estimated car pose are used by a path planner to create possible paths trough the track. To be able to determine the correct trajectory, a heuristical approach is taken based on analysis of previous Formula Student tracks. We show how time-critical parts of the system are able to operate at a latency of less than 25 ms and can reconstruct the entire map with errors of just a few centimeters. This allows for path planning in real-time at high speed close to the maximum sensor range.