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This page contains a short introductory lecture on Brownian motion. In this lecture we introduce Brownian motion, a model for random motion of a particle in continuous time, i.e. a continuous version of a random walk. Such motion was first described by Robert Brown in 1827 when he observed the random wiggling of pollen suspended in water (here is a video showing the effect). Promoted by Einstein it provided evidence of the existence of molecules as discrete constituents of water that randomly bump into the pollen particles to create the observed motion. Nowadays, Brownian motion is used to mathematically describe a vast variety of phenomena, ranging from fluctuations in stock prices to diffusion of ink in water.