You can apply a Path Tools effect by clicking the Extra menu and expanding the Path Tools group.
Unites the objects.
Results in an object which is the overlap of the original objects.
Exclude Intersected Areas
Results in an object which is the union of the original objects minus their overlaps.
Results in an object which is the bottom object minus the other objects.
Subtract Front Shape
Removes all overlaps and self-intersections.
Add Control Points
Points are added to the objects where they intersect the other objects.