Explore the fascinating world of Higgs bundles in this comprehensive lecture by Laura Schaposnik at the International Centre for Theoretical Sciences. Delve into the concept of spectral data and its application to Higgs bundles, a crucial component in modern mathematical physics. Learn about the intricate connections between Higgs bundles, Yang-Mills equations, and their role in various mathematical theories including the Geometric Langlands Program and Mirror Symmetry. Gain insights into the rich geometric structures of Higgs bundle moduli spaces and their significance in physical theories. This hour-long talk is part of a broader program featuring short courses and lectures by renowned experts in the field, offering a deep dive into this complex and influential area of mathematics and theoretical physics.