This course is a first hands-on introduction to stochastic modeling. Examples will mostly come from the area of Financial Mathematics, so that this course plays a central role in the education of students interested in Quantitative Finance and Mathematical Economics. Topics include binomial tree models, discrete Brownian paths, stochastic ODEs, Monte-Carlo methods, finite differences solutions for the Black-Scholes equation, and an introduction to time series analysis, parameter estimation, and calibration. We program and explore all basic techniques in a numerical programming environment and apply these algorithms to real data whenever possible