Nikon D610 has a Nikon F lens mount and currently there are 278 native lenses available for this mount.
Nikon D610 doesn't have a sensor based image stabilization system but 55 of these lenses already comes with optical image stabilization.
Since Nikon D610 has a Full frame sensor, it has a focal length multiplier of 1× so lenses will provide their original focal length on D610.
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Nikon D610 Lenses with Image Stabilization
Nikon D610 Lenses with Weather Sealings