Napoleonic
Napoleon Bonaparte did many things to change the nature of warfare. Napoleon's single greatest legacy in warfare was the extensive use and elaboration of the disseminated army; he separated groups of units in his army to spread them out over a wider area but kept them under his central command unlike in earlier times when each separate division would have fought independently. This allowed him to force battle by turning or encircling the enemy army where in previous eras armies only fought by mutual consent or because a surprise manoeuvre had them trapped against an obstacle such as a river.
He relied heavily on the column, a formation less than a hundred men wide and containing an entire brigade in tight formation and mostly advanced to contact with the bayonet. The constant movement and sheer mass of this formation could break through most enemy lines, but was susceptible to being broken by well drilled or large volumes of fire as it could not fire as it advanced. Its main advantage was its ability to march rapidly and then deploy into line comparatively easily, especially with well drilled and motivated troops such as those available to Napoleon after the French Revolution. He later utilised the Mixed Order formation which could be a combination of one or more lines supported by one or more columns. This offered the extended firepower of the line with the rapid reaction ability of the column in support.
The column formation allowed the unit rapid movement, a very effective charge (due to weight of numbers) or it could quickly form square to resist cavalry attacks, but by its nature only a fraction of its muskets would be able to open fire. The line offered a substantially larger musket frontage allowing for greater shooting capability but required extensive training to allow the unit to move over ground as one while retaining the line.
The mixed order remained a part of French tactical doctrine as the French army grew in discipline, capitalising as it did on the strengths of both the line and column formations, while avoiding some of their inherent weaknesses. It was used extensively by Napoleon when commanding the Grande Armée.
This greatly surpassed other armies at the time which had to move slowly to keep their lines aligned and coherent and as such keep the cavalry from their interior; spaces could be guarded with musket fire, but the line had to be generally aligned and this could be lost over even apparently flat undulating ground as individuals slowed or sped up across uneven ground. The only antidote was slow movement and the column afforded tactical battlefield manoeuvrability and as such a chance to outflank or outmanoeuvre the enemy, or, more importantly, concentrate against weaknesses in the enemy lines.
Napoleon was also an avid user of artillery - he began his career as an artillery officer - and used the artillery to great effect due to his specialist knowledge. The French army after the French Revolution was greatly motivated and after the reforms of 1791, well trained in the newest doctrine.
His enemies eventually defeated Napoleon, but his tactics were studied well into the 19th Century, even as improved weapons made massed infantry attacks increasingly hazardous.
Column, due to its manoeuvrability and ease of control, were also used against natives in lands being colonized by Europeans during the late 19th Century.
Read more about this topic: Infantry Tactics