Which level of government has the greatest authority?

Assuming we are talking about US Government?

The Executive Branch has authority overall. All bills passed through Legislative still need to go to Excutive (president) to be signed or vetoed. However, the president cannot make laws so the Legislative branch is very powerful but does not have the greatest authority

battle of saint-mihiel, (12–16 september 1918), allied victory and the first u.s.-led offensive in world war i. the allied attack against the saint-mihiel salient provided the americans with an opportunity to use their forces on the western front en masse.

explanation:

on the morning of  july 21,  1861, general mcdowell ordered the  unionarmy to attack. it was on this hill that  confederate  colonel thomas jackson and his forces held back theunion  troops.