Superconducting Magnetic Energy Storage (SMES) offers many advantages over conventional forms of energy storage. The higher unit costs of SMES make it economically feasible only for large-scale applications (5000 MWh or more). Early studies showed that low aspect ratio solenoids have the lowest overall costs and most of the subsequent research and conceptual design was centered around low to moderate aspect ratio solenoidal designs. Toroids, poloids and force-reduced magnets are some alternate magnet structures that can be used for SMES but have not received much attention. These structures have some advantages over solenoidal designs such as lower peak fields with greater energy storage capability (poloid), lower support structure requirement (force-reduced magnet) and zero external field (toroid). For some applications of SMES such as pulsed power for fusion reactors or particle accelerators, where the large external field of the solenoid may be unacceptable but the fast response and high efficiency of SMES are required, alternate magnet structures or geometries must be used even if the costs are somewhat higher. Therefore it is useful to study the relative costs of each magnet structure in order to choose a suitable magnet structure for a given application. Four magnet structures viz. the solenoid, toroid, poloid and a force-reduced magnet are evaluated for their energy storage capability, support structure requirements and stray field characteristics. The variation of these parameters with the geometry of the magnet as well as the size of the SMES system are also studied. The objective of this study is to provide a quantitative comparison of important magnet parameters as well as to develop a simple procedure for the preliminary magnetic design of SMES magnets of any size, based on the detailed analysis of a reference design. Due to the high costs of SMES particularly for smaller sizes, it is important to optimize magnet design as well as to look for new magnet configurations to make SMES more cost effective. Superconductor and support structure material are major components of the overall cost of SMES magnets. Various methods of optimizing these parameters are explored. Force-reduced magnets have attracted some controversy in SMES research due to various claims made for and against them. The virial theorem and its implications for force-reduced magnets are analyzed with reference to a specific force-reduced configuration and it is shown that the claims that force-reduced magnets do not offer any savings in structure are unjustified. Methods for further reducing the structure requirements in force-reduced magnets and toroidal magnets are discussed. Due to the unique and highly desirable characteristic of zero stray field of toroidal magnets, it is important to seek ways of increasing its energy storage capability. A variational problem is formulated to determine the optimal cross-sectional shape which maximizes the stored energy with a given quantity of superconductor. The optimal shape stores 16 p.c. more energy than the circular cross section toroid and is shown to be identical to the structurally superior constant tension D shape. The desired characteristics of an ideal SMES magnet are shown to be a uniform magnetic field within a closed magnet configuration. A twisted toroidal magnet combining the features of an ideal solenoid and the general toroidal configuration is studied as a candidate for the ideal magnet. Geometric arguments are used to prove that no such closed surface can be found in three dimensions with the minimum smoothness conditions required from physical considerations. / Ph. D.