Explore the fundamental concepts of additive combinatorics in this 54-minute lecture by David Grynkiewicz from the International Centre for Theoretical Sciences. Delve into set addition and sum sets before examining basic lower bounds and Kneser's Theorem. Follow along as the speaker presents and proves key theorems, including the Cauchy-Davenport theorem from 1813. Gain insights into special cases like complete torsion and field extensions. This talk, part of a workshop on Additive Combinatorics, offers a comprehensive introduction to essential topics in this dynamic field that intersects with number theory, ergodic theory, and harmonic analysis.