What is the name of the event where the union army under general ulysses s. grant, gained greater control of the mississippi river?

Union General Ulysses S. Grant advances toward the Mississippi capital of Jackson during his bold and daring drive to take Vicksburg, the last Confederate stronghold on the Mississippi River.

The answer is Siege of Vicksburg

By capturing Vicksburg, the last major river-port in Confederate hands. It was almost impossible to attack the high-lying town from the West bank where Grant had been ordered to march against his will. Through brilliant diversionary tactics, he was able to cross the river downstream, without the commander of the garrison noticing. Then he brought the Confederates to battle, helped by the bad situation of the garrison commander, who was receiving conflicting orders. It should be noted that the siege on Vicksburg was the Union's third and final attempt to capture this important city.

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