Quantitative science is impossible without measuring and analyzing signals. Examples include time-dependent voltages in electric circuits, microscopy images of nanostructures, pressure variations in blood vessels as well as electromagnetic and acoustic waves in matter. This lecture course will provide an introduction into the toolbox of signal analysis and its applications. Questions that will be addressed are for example: How can we measure a small signal that is buried in a large noise background? How does a lock-in amplifier work? How can we reconstruct a continuous signal that was sampled only at discrete times? What are aliasing and undersampling? How can we characterize as diverse systems as electrical filters, light detectors and optical lenses by a single formalism? Why is Fourier analysis such a powerful tool here? In the exercises, the course topics will be illustrated by practical examples, both analytical and numerical.