1) The document discusses basic practice calculations involving scalar fields in quantum field theory, including evaluating vacuum-to-vacuum transition matrices. 2) It presents the path integral formulation for evaluating these matrices in the absence of self-interaction terms, and how inserting an exponential potential operator handles self-interaction terms. 3) Notation is introduced for representing terms involving sources, propagators, and derivatives in a clear way when evaluating expressions like the vacuum-to-vacuum transition matrix with self-interactions.