This is an abridgement of Barr and Diamond's 'Reforming Pensions: Principles and Policy Choices' (OUP, 2008), a larger book that is intended for policy makers and as a supplement in college courses. The problem. Mandatory pension systems are a worldwide phenomenon. However, with given contribution rates, monthly benefits and retirement ages, pension systems are not consistent with three long-run trends - declining mortality, declining fertility, and earlier retirement. Thus many systems need reform. Principles. This book gives an extensive but nontechnical explanation of the economics of pension design. The theoretical arguments have three elements. 1. Pension systems have multiple objectives - consumption smoothing, insurance, poverty relief, and redistribution. Good policy needs to bear them all in mind. 2. Good analysis should be framed in a second-best context - simple economic models are a bad guide to policy design in a world with imperfect information and decision-making, incomplete markets and taxation. 3. Any choice of pension system has distributional consequences, which the book recognizes explicitly. The analysis includes discussion of labor markets, capital markets, risk sharing and gender and family, with comparison of PAYG and funded systems, recognizing that the suitable level of funding differs by country. Alongside the economic principles of good design, policy must also take account of a country's capacity to implement the system. Thus the theoretical analysis is complemented by discussion of implementation, and of experiences, both good and bad, in many countries, with particular attention to China and Chile. Policy conclusions: 1. Sound application of the principles outlined above can and does lead to widely different systems in different country settings. 2. Unless there are transfers from outside the system, any improvement to the finances of a pension system must involve one or more of (a) higher contribution rates, (b) lower monthly pensions, (c) later retirement at the same monthly pension, (d) policies designed to increase national output. 3.The previous statement holds whatever the degree of funding. If a public pension is regarded as unsustainable the problem needs to be addressed directly by one of these methods.