The Thurston norm is a mathematical concept used in the field of topology, particularly in the study of 3-manifolds. It provides a way to measure the complexity of a surface within a 3-manifold by assigning a non-negative real number to each homology class. This norm helps in understanding how surfaces can be embedded and how they interact with the manifold's structure. Developed by mathematician William Thurston, the norm is significant in the classification of 3-manifolds and plays a crucial role in geometric topology. It aids in distinguishing between different types of manifolds and surfaces, contributing to the broader understanding of their geometric properties.