Olympus E-M1 has a Micro Four Thirds lens mount and currently there are 121 native lenses available for this mount. E-M1 also has a sensor based image stabilization system which means that all of these lenses will be stabilized when used on the E-M1.
Since Olympus E-M1 has a Four Thirds sensor, it has a focal length multiplier of 2� 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-M1.
You may also also be interested in these:
Olympus E-M1 Lenses with Image Stabilization
Olympus E-M1 Lenses with Weather Sealings