The KArlsruhe TRItium Neutrino experiment (KATRIN) aims to measure the electron neutrino mass with an unprecedented sensitivity of 0.2 eV/c2, using β-electrons from tritium decay. Super-conducting magnets will guide the electrons through a vacuum beam-line from the gaseous tritium source through a differential pumping section to a high resolution spectrometer, where the kinetic energy will be measured. This paper will give an overview of the complex vacuum system of the KATRIN experiment and presents first results of the vacuum performance of the spectrometer. Background considerations require a vacuum of 10-11 mbar or better in the large spectrometer vessel (1240 m3). A combination of NEG pumps and cascaded turbo-molecular pumps will provide the necessary pumping speed. First measurements of outgassing rates after baking the stainless steel vessel (316LN) at 350°C are reported here.