Explore the foundations of signal and image analysis in this first lecture of a series delivered by renowned mathematician Ingrid Daubechies at the 2020 Joint Mathematics Meetings. Delve into the mathematical frameworks underpinning multiresolution analysis, wavelets, and advanced techniques in the field. Gain insights from Duke University's expert as she presents the American Mathematical Society Colloquium Lecture, offering a comprehensive introduction to these crucial concepts in modern mathematics and their applications in signal processing and image analysis.