An introduction to wavelet analysis with a focus on applications. Wavelets are an important tool in modern signal and image processing as well as other areas of applied mathematics. The main objective of this course is to develop the theory behind wavelets and similar constructions. Theoretical topics may include Fourier analysis, the discrete and continuous wavelet transform, Shannon's Sampling Theorem, statistical studies of wavelet signal extraction, and the Heisenberg uncertainty principle. Application based topics may include wavelet based compression, signal processing methods, communications, and sensing mechanisms where wavelets play a crucial role. Students will gain hands-on experience with real-world imaging techniques.