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If you would like to browse the contents of a snapshot, select that snapshot in the snapshots table, then right-click and choose the Browse in Finder option. Or, simply double-click on the snapshot. You may then browse the contents of that snapshot in the customary manner in the Finder. The snapshot is mounted read-only, so it is impossible for you to make any harmful modifications to the snapshot. If you would like to restore a single item, you can simply drag the item from the snapshot to wherever you want to restore it to. When a snapshot is mounted, the creator icon of the snapshot in the Snapshots table will have a green dot to indicate that it is mounted.
Note: Neither the Finder nor Disk Utility shows mounted snapshots by default, so you cannot typically unmount a snapshot in those applications. CCC will indicate when a snapshot is mounted by placing a small green dot on the snapshot creator icon in the snapshots table. You can right-click on a mounted snapshot in CCC and choose the Unmount option to manually unmount a snapshot. For your convenience, however, CCC will automatically unmount any snapshots that it mounted when you quit CCC.