Robotic rehabilitation has gained significant traction in recent years, due to the clinical demonstration of its efficacy in restoring function for upper extremity movements and locomotor skills, demonstrated primarily in stroke populations. In this thesis, I present the design of MAHI Exo-II, a robotic exoskeleton for rehabilitation of the upper extremity after stroke, spinal cord injury, or other brain injuries. The five degree-of-freedom robot enables elbow flexion-extension, forearm pronation-supination, wrist flexion-extension, and radial-ulnar deviation. In the first part of this thesis, hardware design of the system is presented. The device offers several significant design improvements compared to its predecessor, MAHI Exo I. Specifically, issues with backlash and singularities in the wrist mechanism have been resolved, torque output has been increased in the forearm and elbow joints, a passive degree of freedom has been added to allow shoulder abduction thereby improving alignment especially for users who are wheelchairbound, and the hardware now enables simplified and fast swapping of treatment side. These modifications are discussed in the thesis, and results for the range of motion and maximum torque output capabilities of the new design and its predecessor are presented. In the second part of this thesis. I present the modification and implementation of a previously reported linear position and force control to MAHI Exo-II. The modified controller includes three different modes which are designed for use with patients with different levels of severity of injury. These modes either completely assist or resist the patient during the movement. Next, I present the implementation of a previously proposed nonlinear control algorithm in simulation for the forearm and wrist module of MAHI Exo-II. The proposed nonlinear controller aims to provoke a compliant characteristic to the device and assist the patient only as much as needed. Finally, the result of clinical testing of the feasibility of the mechanical design and the efficacy of the control modes with a 28-year-old female SCI patient are presented.