In this paper, we present the MESSII Dataset (Manipulator Experimental SyStem Identification and Interaction Dataset). This novel dataset aims at providing numerous sequences of movements of the KUKA iiwa manipulator, in order to evaluate methods for identification and estimation of the robot's dynamic parameters and signals, respectively. Different movements of the manipulator are provided, including trajectories moving one or multiple joints at the same time, trajectories that are specially designed for parameter identification, and trajectories including a payload attached at the end-effector of the manipulator. The information obtained from the propioceptive sensors of position and torque is presented. Furthermore, as physical Human-Robot Interaction (pHRI) is the main application of this robot, sequences with interaction with a person are provided to estimate the forces applied, where a force-torque sensor acts as the ground truth. The dataset can also be used in ROS to evaluate real-time methods as information is presented in rosbags files. Possible applications are given, highlighting the advantage of the dataset to help with state-of-the-art challenges, without the need of the real robot nor doing new and complex experiments. The dataset, as well as more information and tools, are publicly available in https://messii-dataset.enit.fr.