This lecture delves into the inner workings of the Stainless framework, focusing on verification-aware transformations, dependent type checking, and the Inox counterexample-finder. It explains the principles behind Stainless transformations, termination checking, and SMT embedding, emphasizing the importance of call unfolding for soundness and completeness. The lecture also covers inductive reasoning and the limitations of Stainless, along with its theoretical foundations formalized in Coq.