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We report the design and fabrication of three-dimensional integrated mode couplers operating in the C-band. These mode-selective couplers were inscribed into a boro-aluminosilicate photonic chip using the femtosecond laser direct-write technique. Horizontally and vertically written two-core couplers are shown to allow for the multiplexing of the LP11a and LP11b spatial modes of an optical fiber, respectively, with excellent mode extinction ratios (25-37 + dB) and low loss (~1 dB) between 1500 and 1580 nm. Furthermore, optimized fabrication parameters enable coupling ratios close to 100%. When written in sequence, the couplers allow for the multiplexing of all LP01, LP11a and LP11b modes. This is also shown to be possible using a single 3-dimensional three-core coupler. These integrated mode couplers have considerable potential to be used in mode-division multiplexing for increasing optical fiber capacity. The three-dimensional capability of the femtosecond direct-write technique provides the versatility to write linear cascades of such two- and three-core couplers into a single compact glass chip, with arbitrary routing of waveguides to ensure a small footprint. This technology could be used for high-performance, compact and cost-effective multiplexing of large numbers of modes of an optical fiber.