Explore the applications of crystal base theory in this comprehensive lecture from the Workshop on Integrable systems, exactly solvable models and algebras. Delve into the combinatorial definition of crystals and discover their applications in symmetric functions and cyclic sieving. Learn how crystal bases play a crucial role in statistical mechanics, representation theory, and combinatorics. Gain insights from expert Anne Schilling as she continues her in-depth exploration of this fascinating mathematical topic in the second part of her presentation.