The structure of the tetracene/Ag(111) interface in the coverage range θ = 0 to 2.4 ML is studied with scanning tunneling microscopy (STM) at 8 K and with low energy electron diffraction (LEED) at T = 300 . . . 100 K. For θ 0.01 ML, one-dimensional (1D) diffusion of single molecules along 011 -directions is observed even at 8 K. For 0.1 ML < θ < 0.5 ML molecules are homogeneously distributed over the surface forming a disordered phase (static at T = 8 K, dynamic at T = 25 K), indicating a repulsive intermolecular interaction (δ-phase). For θ 0.5 ML, local ordering in the commensurate γ -phase is observed. Further increase of the coverage yields a compressed monolayer (ML) phase (θ ≡ 1 ML) with point-on-line registry (α-phase). The interaction between molecules has been calculated with the force-field approach to rationalize the molecular packing motifs in the various phases. Under most circumstances molecule-molecule interactions are repulsive, in agreement with experimental findings. A simulation of the adsorption up to θ = 1 ML according to the random sequential adsorption (RSA) algorithm shows that the disorder-to-order transition from the δ-to γ -phase occurs close to random close packing (RCP), θ = 0.5-0.6 ML. Since tetracene molecules are a two-dimensional (2D) representation of Onsager's hard rod model, this suggests that this phase transition is driven both energetically and entropically. For θ ≈ 2.23 ML a metastable bilayer phase with point-on-line coincidence is observed (β-phase). The basic structural unit of this phase is a triplet of molecules that are tilted along the long molecular axis against each other; at least one of these molecules is tilted out of the surface plane. Within the β-phase a superstructure of alternating rotation domains is observed. This superstructure has a period of 7.4 nm. The molecular packing in the β-phase resembles the packing in the bulk crystal structure of tetracene, its formation can therefore be interpreted as incipient pseudomorphic growth of tetracene on Ag(111). However, pseudomorphic growth cannot be continued beyond the β-phase.