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This paper is intended to pave the way for new researchers in the field of robotics and autonomous systems, particularly those who are interested in robot localization and mapping. We discuss the fundamentals of robot navigation requirements and provide a review of the state of the art techniques that form the bases of established solutions for mobile robots localization and mapping. The topics we discuss range from basic localization techniques such as wheel odometry and dead reckoning, to the more advance Visual Odometry (VO) and Simultaneous Localization and Mapping (SLAM) techniques. We discuss VO in both monocular and stereo vision systems using feature matching/tracking and optical flow techniques. We discuss and compare the basics of most common SLAM methods such as the Extended Kalman Filter SLAM (EKF-SLAM), Particle Filter and the most recent RGB-D SLAM. We also provide …