Olympus E-M10 has a Micro Four Thirds lens mount and currently there are 132 native lenses available for this mount.
The latest released lenses that are compatible with the E-M10 are the Brightin Star 60mm f2.8 II, the 7Artisans 50mm f1.2 APS-C and the Pergear 50mm F1.2 APS-C.
E-M10 also has a sensor based image stabilization system which means that all of these lenses will be stabilized when used on the E-M10.
Since Olympus E-M10 has a Four Thirds sensor, it has a focal length multiplier of 2x so you have to multiply lenses original focal length with this multiplier to find the Full Frame equivalent focal length of the lens when mounted on E-M10.
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Olympus E-M10 Lenses with Image Stabilization
Olympus E-M10 Lenses with Weather Sealings