The Fourier transform from the time-domain to the frequency-domain is a powerful tool for an abundance of applications. In this lecture, the focus is on that of finance and risk. A brief introduction to the Fourier transform is given, and then an introduction to three motivating examples from my own research: 1. Likelihood estimation of stochastic differential equations with jumps. 2. Aggregating non-life risks and premium principles with KPI-target control. 3. Information efficient data-driven model selection in machine learning.