We demonstrate the emergence of altermagnetism at the surfaces of antiferromagnets, vastly expanding the number of material candidates with altermagnetic characteristics and establishing a route towards two-dimensional altermagnetism through surface-induced symmetry breaking. We do so by developing a formalism that fully classifies all surface magnetic states and identifies altermagnetic surface spin groups that can arise at the surfaces of antiferromagnets. We use this formalism to identify over 150 antiferromagnetic entries from the MAGNDATA database with at least one altermagnetic surface, often times with multiple such surfaces in the same material, and clarify the role of surface roughness and terraces. We illustrate this emergent phenomenon in a realistic Lieb lattice-based minimal model and present calculations on two representative material candidates, NaMnP and FeGe 2 , exhibiting d -wave and g -wave surface altermagnetism, respectively. Our theory naturally resolves the contradiction of recent experimental reports of d -wave spin splitting from ARPES measurements on metallic Lieb lattice compounds such as KV 2 Se 2 O that have been shown to be antiferromagnetic in the bulk. Hence, we establish a new paradigm for generating effectively two-dimensional altermagnetism by functionalizing the abundant material class of collinear antiferromagnets as viable platforms for controlled surface altermagnetism.