What is the cause of the battle of Waterloo?

Answer 1

The return of Napoleon from Elba leads to the Hundred days campaign. A model of its former excellence this was only to fail during the day of the battle. Wellington had picked his site well....

I would like to improve the answer as follows.

Napoleon's escape from Elba and his successful attempt to regain the power in a very short time alarmed all the European Courts, leading to an immediate mobilization of their armies.

Napoleon claimed he had but no hostile intention towards none of the European Nations and he wanted only rule France according to the clear wish expressed by the French people immediately after his return. But in vain: the mobilization went on and the first two allied armies, those of Great Britain and Prussia were deploying their troops through the Belgium.

The general strategical plan of the Allied Coalition foresaw to concentrate the most possible of their armies before getting engaged in the hostilities and the proceed to invade France, as they had already done in the campaign of 1814. In so doing they would have again had such a numerical superiority over Napoleon's army to secure them the victory.

But Napoleon forestalled that plan and invaded Belgium, defeating the Prussians at Ligny, thus dividing them from the British and forcing Wellington to fight at Waterloo.