  We introduce $\phi^4$ interacting real scalar Quantum Field Theory (QFT) on
causal sets. We consider both the canonical framework of causal set free QFT,
involving a Hilbert space and operators and so on, and the double path integral
framework of causal set QFT outlaid by Sorkin. In both cases we describe how to
extend the formalism to include a $\phi^4$ self-interaction, and, to make
contact with the continuum, we contrast certain key expressions with their
continuum counterparts. We develop a diagram-based algorithm, analogous to
Feynman diagrams in the continuum, to compute the interacting 2-point function
of our causal set QFT. Notably, causality is manifest in our diagrams in a
manner not present in the usual Feynman diagrams of the continuum theory.
