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The Muon Ionization Cooling Experiment (MICE) focusing solenoid magnets focus the muon beam within the MICE cooling channel on a liquid or solid absorber that is within the warm bore of solenoid. The focusing magnet has a warm bore of 470 mm. This magnet consists of two coils 210-mm long that is separated by an aluminum mandrel that is 200 mm long. Each of the coils has its own leads. The coils may be operated in either the non-flip mode (solenoid mode with both coils at the same polarity) or the flip mode (quadrupole focusing mode where both coils are at opposite polarity). This report describes the focusing solenoid magnet design that will be built by the vendor. The progress on the construction of the first of the focusing magnets will also be discussed in this report. Ultimately three of these magnets will be built. These magnets will be cooled using a pair 1.5 W (at 4.2 K) pulse tube coolers.