Axioms for Quantum Yang-Mills Theories -- 1. Euclidean Axioms

This paper extends the notion of Schwinger functions to quantum Yang-Mills theories and proposes the axioms they should satisfy. Two main features of this axiom scheme are that we assume existence of gauge-invariant co-located Schwinger functions and impose physical properties only on them. This is in accordance with the fundamental principle of gauge theories that only gauge-invariant quantities can be physical observables.