Explore quadratic forms, Hermite constants, and reduction theory in this comprehensive lecture on sphere packing. Delve into techniques for computing the densest possible lattice packing, examining the relationship between lattices and quadratic forms. Investigate Hermite constants, extreme lattices, and critical quality forms. Learn about lattice reduction theory, including Lagrange-Seeban-Menkouski reduction and its application to calculating delta for dimensions up to 8. Study perfect forms, weekly eutactic lattices, and the proof connecting extreme forms to perfect forms. Conclude with an overview of Voronoi's algorithm for obtaining a complete list of perfect forms, gaining valuable insights into this fundamental area of geometry and number theory.