The LIght Detection And Ranging (LiDAR) sensor has become one of the most important perceptual devices due to its important role in simultaneous localization and mapping (SLAM). Existing SLAM methods are mainly developed for mechanical LiDAR sensors, which are often adopted by large scale robots... Recently, the solid-state LiDAR is introduced and becomes popular since it provides a cost-effective and lightweight solution for small scale robots. Compared to mechanical LiDAR, solid-state LiDAR sensors have higher update frequency and angular resolution, but also have smaller field of view (FoV), which is very challenging for existing LiDAR SLAM algorithms. Therefore, it is necessary to have a more robust and computationally efficient SLAM method for this new sensing device. To this end, we propose a new SLAM framework for solid-state LiDAR sensors, which involves feature extraction, odometry estimation, and probability map building. The proposed method is evaluated on a warehouse robot and a hand-held device. In the experiments, we demonstrate both the accuracy and efficiency of our method using an Intel L515 solid-state LiDAR. The results show that our method is able to provide precise localization and high quality mapping. We made the source codes public at \url{https://github.com/wh200720041/SSL_SLAM}. (read more)