Methane is a major anthropogenic greenhouse gas, second only to carbon dioxide (CO2) in its impact on climate change. Methane (CH4) has a high global warming potential that is 25 times as large as the one of CO2 on a 100 year time horizon according to the latest IPCC report. Thus, CH4 contributes significantly to anthropogenic radiative forcing, although it has a relatively short atmospheric perturbation lifetime of 12 years. CH4 has a variety of sources that can be small, geographically dispersed, and not related to energy sectors. In this report, we analyze methane emission abatement options in five different sectors and identify economic mitigation potentials for different CO2 prices. While mitigation potentials are generally large, there are substantial potentials at low marginal abatement costs. Drawing on different assumptions on the social costs of carbon, we calculate benefit/cost ratios for different sectors and mitigation levels. We recommend an economically efficient global methane mitigation portfolio for the year 2020 that includes the sectors of livestock and manure, rice management, solid waste, coal mine methane and natural gas. Depending on assumptions of social costs of carbon, this portfolio leads to global CH4 mitigation levels of 1.5 or 1.9 GtCO2-eq at overall costs of around $14 billion or $30 billion and benefit/cost ratios of 1.4 and 3.0, respectively. We also develop an economically less efficient alternative portfolio that excludes cost-effective agricultural mitigation options. It leads to comparable abatement levels, but has higher costs and lower benefit/cost ratios. If the global community wanted to spend an even larger amount of money - say, $250 billion - on methane mitigation, much larger mitigation potentials could be realized, even such with very high marginal abatement costs. Nonetheless, this approach would be economically inefficient. If the global community wanted to spend such an amount, we recommend spreading the effort cost-effectively over different greenhouse gases. While methane mitigation alone will not suffice to solve the climate problem, it is a vital part of a cost-effective climate policy. Due to the short atmospheric lifetime, CH4 emission reductions have a rapid effect. Methane mitigation is indispensable for realizing ambitious emission scenarios like IPCC's "B1", which leads to a global temperature increase of less than 2°C by the year 2100. Policy makers should put more emphasis on methane mitigation and aim for realizing low-cost methane mitigation potentials by providing information to all relevant actors and by developing appropriate regulatory and market frameworks. We also recommend including methane in emissions trading schemes.