With the uncertainties in the implementation of carbon emission reduction, the increase in global mean temperature is likely to exceed the 1.5◦ C target set by the Paris Agreement by the middle of this century. To address this challenge, stratospheric aerosol injection (SAI) is studied here as a possible supplement to emission reduction to reduce the risks associated with climate change. SAI adds aerosols, or their precursors, to the lower stratosphere to reflect a small fraction of the incoming solar radiation back to space, and thus temporarily lowers the global mean temperature. While offsetting global warming, SAI will not bring the climate back to the same state as lowering the CO2 concentration. Instead, it will create a novel climate. The resulting climate depends on the choice of injection strategy, which introduces a design aspect to SAI. For a policy-relevant global cooling of 1-1.5◦ C, there are of order 6-8 degrees of freedom in the SAI design space. This PhD work systematically explores the SAI design space and the range of possible climate outcomes, evaluates the underlying trade-offs, and presents an optimization approach for searching optimal strategies that simultaneously manage more than three independent climate goals.