Abstract: We will introduce the concept of Turing (or diffusion-driven) instability in reaction-diffusion equations. We will focus on reaction-diffusion equations on a sphere. We will aim to compare the results obtained using the methods of linear stability analysis on a sphere with results obtained in other geometrical settings including boundary conditions. We will apply the methods of weakly-nonlinear analysis to further investigate qualitative properties to the solutions on a sphere and compare these with results obtained using linear analysis.