Basics in Energy Finance CEMS Climate change, nuclear phaseout, supply bottlenecks: Economics add to nature, politics, and technology. Join the current discussion well-founded! The global trend in electricity market liberalization has introduced competition into a traditionally monopolistic and regulated business. The markets in Europe are characterized by a heterogeneous mix of technologies, economics, and regulations with complex interdependencies. Production, transmission, and distribution of electricity require efficient planning of operations and investments. The introduction of carbon trading adds even more complexity and uncertainty to the markets. In this setting, established methods from mathematical finance are often not applicable. The transmission and distribution of electricity requires expensive networks with limited capacities. The latter impose physical restrictions on the real-time flows of electricity in contrast to the more or less free money flows in financial markets. Electricity itself is almost non-storable and produced from a diverse portfolio of technologies and fuels. Therefore, it can basically be considered as a commodity with derivative characteristics. In this course, we first introduce the developments and challenges in energy markets. We discuss different electricity market designs and quantitative approaches to evaluate strategies and operations under uncertainty which also require risk related considerations. Manifold stochastic influences must be taken into account, which include price uncertainties for electricity and the underlying fuels as well as physical availability and fluctuations in supply and demand. Examples include the market-driven operation of hydro-power plants as well as complex valuations of financial contracts like futures, options, or swing-options. We demonstrate IT solutions of different scales that can be used for contract evaluations and power management. We also consider the new requirements and possibilities related to the EU Emission Trading System (ETS) including the application of Kyoto mechanisms.