Explore the mathematics behind Noether's Theorems in the calculus of variations in this comprehensive lecture by Prof. Ian Anderson from Utah State University. Delve into symmetries, conservation laws, and variational principles, covering topics such as external and internal symmetries, classical conservation laws, and the Noether Theorems. Examine the Taken's Problem, an inverse Noether Theorem, and investigate invariant variational problems and differential invariants. Learn about the applications of these concepts in various fields, including general relativity, differential geometric structures, and Penrose's Conformal Cyclic Cosmology programme. This lecture is part of the SCREAM project, focusing on Cartan and parabolic geometries and their interactions with mechanical systems, integrable systems, and more.