Democracies are distinguished among political systems by the use of non-violent methods for the resolution of social disagreements, but do not preclude and, in fact, encourage organized action to influence social policy. The course aims to provide a cohesive treatment of mathematical models of key democratic processes with particular attention paid to legislative/parliamentary policy-making; electoral competition and voter participation; and coalition and party formation. Precedence will be placed on dynamic models and on models that are actionable, in the sense that they are amenable to analytical or numerical computation. Suitable methods and algorithms for numerical analysis will be covered in depth when appropriate. The course is designed primarily for PhD students in Political Science, but advanced undergraduate students with mathematical background are also welcome (with instructor permission).