This thesis examines theoretically the potential of the plasma confinement device known as a Stellarator as a fusion reactor. Chapter one contains a survey of the requirements for nuclear fusion to take place in a device employing magnetic confincment. The range of reactor parameters which are appropriate is- derived, both from the point of view of plasma physics and on the basis of a rather crude economic model. Chapter two begins with a discussion of the equilibrium of plasma in Stellarators. Solutions of the equilibrium equations are obtained, employing an Inverse aspect ratio axpansicn of the field quantities. Chapter three Indicates which macroscopic" instabilities are cause for concern in Stellarators without net longitudinal currant. A. stability criterion appropriate to Stellarators is evaluated, using the equilibrium fields found in the proceeding chapter. Chapter four is devoted to the study of the effects of particles which are localised in the ripple of the Stellarator masnetic field on transport. A random walk theory of their contribution to diffusion is given. Chapter five contains a description of the coil systems capable of generating fitellarator fields, and their properties. Specialising to "twisted" coils, geometrical scaling laws are sought, which describe the properties of the fields they produce. Chapter six is a brief indication as to how such coils may be incorporated into a reactor. Chapter seven considers the parameters of a Stellarator reactor based on "twisted" coils, and shows how they may be written in terms of the raajor and minor radii of the device. An economic model of the reactor is given, which allows us to optimise the reactor, to obtain the cheapest system at fixed total power output and wall loading. The result is shown Co be considerably less expensive than similar Tokamak designs.