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Three-dimensional (3D) topologicalWeyl semimetals (TWSs) represent a state of quantum matter with unusual electronic structures that resemble both a ‘3D graphene’ and a topological insulator. Their electronic structure displays pairs of Weyl points (through which the electronic bands disperse linearly along all three momentum directions) connected by topological surface states, forming a unique arc-like Fermi surface (FS). Each Weyl point is chiral and contains half the degrees of freedom of a Dirac point, and can be viewed as a magnetic monopole in momentum space. By performing angle-resolved photoemission spectroscopy on the non-centrosymmetric compound TaAs, here we report its complete band structure, including the unique Fermi-arc FS and linear bulk band dispersion across the Weyl points, in agreement with the theoretical calculations^,. This discovery not only confirms TaAs as a 3DTWS, but …