Olympus E-M10 has a Micro Four Thirds lens mount and currently there are 92 native lenses available for this mount.
E-M10 also has a sensor based image stabilization system which means that all of these lenses will be stabilized when used on 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.
You may also also be interested in these:
Olympus E-M10 Lenses with Image Stabilization
Olympus E-M10 Lenses with Weather Sealings