Canon 77D has a Canon EF/EF-S lens mount and currently there are 319 native lenses available for this mount.
Canon 77D doesn't have a sensor based image stabilization system but 107 of these lenses already comes with optical image stabilization.
Since Canon 77D has a APS-C sensor, it has a focal length multiplier of 1.6× 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 77D.
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Canon 77D Lenses with Image Stabilization
Canon 77D Lenses with Weather Sealings