This chapter introduces the quantum mechanics of interacting field theories, moving beyond free (non-interacting) scalar fields. It begins by classifying the coupling constants of weakly-interacting scalar fields as relevant, irrelevant, or marginal based on their mass dimension in four-dimensional spacetime. The text then presents two fundamental examples: the \(\lambda \phi ^4\) theory and a Scalar Yukawa theory. The theoretical basis for calculating quantum amplitudes is established by reviewing the Interaction Picture and deriving Dyson’s equation. The chapter then defines the S-matrix and demonstrates a leading-order perturbation theory calculation for pion decay in the Scalar Yukawa model, highlighting momentum and energy conservation. Finally, to facilitate higher-order calculations, the powerful tool of Wick’s Theorem is introduced to relate time-ordered products of fields to normal-ordered products and propagators.