Olympus E-M10 has a Micro Four Thirds lens mount and currently there are 125 native lenses available for this mount.
The latest released lenses that are compatible with the E-M10 are the Rokinon 7.5mm f3.5 Fisheye, the Samyang 7.5mm F3.5 Fisheye MFT and the OM SYSTEM 9-18mm f4.0-5.6 II.
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