A compact Butler matrix consists a planar multilayer structure comprising N parallel metal plate waveguides PPW, stacked one on top of the other, two adjacent waveguides PPW comprising a common wall consisting of one of the metal plates. The couplers, the phase-shifters and the crossover devices of the Butler matrix consist of metasurfaces incorporated in the metal plates. The planar two-dimensional beam-former can comprise a Butler matrix with waveguides PPW associated with optical lenses incorporated in each waveguide PPW. Alternatively, the planar two-dimensional beam-former can comprise an upper stage consisting of a Butler matrix with waveguides PPW, and a lower stage comprising waveguides PPW equipped with incorporated reflectors, the two stages being connected in series.