This lecture, the first in the Zygmund Calderón Lectures in Analysis (2025) series, features MIT's David Jerison exploring "How Curved are Level Sets of Solutions to Elliptic PDE? - Part 1." Delve into a new geometry of level sets of semilinear elliptic equations (δ(u) = f(u)), inspired by Hamilton and Perelman's work on mean curvature flow and Ricci flow. Learn about potential applications to level sets of eigenfunctions, beginning with harmonic functions. Discover two fundamental tools of algebraic and differential geometry: Jacobi functions and the Levi-Civita affine connection. Presented by the University of Chicago Department of Mathematics, this one-hour lecture offers valuable insights for those interested in advanced mathematical analysis.