Stroke is a leading cause of disability worldwide, and much attention has been focused to technologies to aid in recovery. This thesis details the design of a dexterous hand exoskeleton for use in stroke patient rehabilitation exercises. This device is able to accommodate a wide range of users and can be adjusted to support a number of different grasping motions. The features that allow this versatility are explained. The exoskeleton is actuated through a Bowden cable system and employs an admittance control strategy. The kinematics-based optimization created to design the manipulator links is presented in detail.