Chances are you may have to strip the top and refinish.
Pic #1 has a white ring on the right side. Apply some mayonnaise to the ring for an hour or so, rubbing it in periodically.... see if the ring disappears. After the 1 hour treatment, clean off the mayo with mild soap and water. If some of the ring disappears, repeat the treatment.
Next: There are large areas where the surface is "cloudy", meaning the sheen or finish has been affected. We can't tell if those areas have a rough feel to them, hence no way to surmise what caused the problem. I'm kinna wondering if someone cleaned those areas with a Scotch Brite type pad and the result is removal of the finish's sheen in those areas. After the mayo treatment is complete, lightly sand the whole top with 220 grit sandpaper and clean off the dust.
In pic #2 the left bottom edge has a blemish on/in the finish(?). The previous light sanding may help with any subsequent resolution of this issue.
So, this is three different issues and a one simple fix may likely not be what is required. All three issues are likely caused by three different circumstances. Do the light sanding and the mayo treatment, then re-evaluate the results before deciding what next to do.