1. Introduction; 2. Optimal linear labour income taxation; 3. The optimal nonlinear labour income tax; 4. Optimal top marginal rates and quasi-linear preferences in consumption; 5. Numerical optimal nonlinear tax schedules; 6. Optimal separable capital income and labour income taxation; 7. The empirical relationship between the extent of redistribution and the components of the Mirrlees framework; 8. Other considerations on redistribution; 9. Conclusions.