In this paper we establish a monolayer of Mn on W(110) as a model system for two-dimensional itinerant antiferromagnetism. Combining scanning tunneling microscopy (STM), low-energy electron diffraction, and ab initio calculations performed with the full-potential linearized augmented plane wave method we have studied the structural, electronic, and magnetic properties of a Mn monolayer on W(110). Our experimental results indicate that in spite of the huge tensile strain Mn grows pseudomorphically on W(110) up to a thickness of three monolayers. Intermixing between the Mn overlayer and the W substrate can be excluded. Using these structural data as a starting point for the ab initio calculations of one monolayer Mn on W(110) we conclude that (i) Mn is magnetic and exhibits a large magnetic moment of 3.32μB, (ii) the magnetic moments are arranged in a c(2 X 2) antiferromagnetic order, (iii) the easy axis of the magnetization is in plane and points along the [11̄0] direction, i.e., the direction along the long side of the (110) surface unit cell with a magnetocrystalline anisotropy energy of 1.3-1.5 meV, and (iv) the Mn-W interlayer distance is 2.14 Å. The calculated electronic structure of a Mn monolayer on W(110) is compared with experimental scanning tunneling spectroscopy results. Several aspects are in nice agreement, but one cannot unambiguously deduce the magnetic structure from such a comparison. The proposed two-dimensional antiferromagnetic ground state of a Mn monolayer on W(110) is directly verified by the use of spin-polarized STM (SP-STM) in the constant-current mode, and an in-plane easy magnetization axis could be confirmed using tips with different magnetization directions. We compare the measurements with theoretically determined SP-STM images calculated combining the Tersoff-Hamann model extended to SP-STM with the ab initio calculation, resulting in good agreement.