An event camera has independent pixels that sends information, called “events” when they perceive a local change of brightness. The information is transmitted asynchronously exactly when the change occurs, with a microsecond resolution, making this sensor suitable for fast robotics applications. We present two new tracking and mapping algorithms, designed to work in parallel to estimate the 6 DOF (Degrees Of Freedom) trajectory and the structure of the scene in line based environments. The tracking thread is based on a Landmark Based map and an asynchronous EKF (Extended Kalman Filter) filter to estimate event per event the state of the camera unlocking the true potential of the camera. Inside the mapping thread, a line extraction algorithm has been designed to find 3D segments in the Point cloud, computed using event – ray tracing into a discretized world. Both algorithms have been built from scratch, and at this moment, only tested independently in simulation. We have obtained very good results on three synthetic self-made datasets. Some pieces of the complete Parallel Tracking and Mapping system are still missing. The current good work and results encourages to improve and finish the algorithm to achieve the implementation on the real event based camera.