Occupancy Grid Map algorithm to map an environment.
For Simultaneous Localization and Mapping a lot of algorithms exist. This post shows the basics of SLAM and how Grid-based FastSLAM works using ROS.
Monte Carlo Localization Algorithm and C++ Implementation
The Kalman filter is used for state estimation and sensor fusion. This post shows how sensor fusion is done using the Kalman filter and ROS.
The Kalman filter is used for state estimation but limited to linear models. To deal with nonlinear models the extended Kalman filter can be used instead.