After the introduction of the tank in WW1, what effect did their introduction have on how battles were carried out, and strategies were formulated?
Ironically, even though tanks were introduced in 1916 (at the battle of the Somme), they had little impact on World War I. They did not break up the trench warfare of the time (even though they were designed to do that).
It was during the period BETWEEN the two world wars, that generals thought about tanks. The British expert was Basil Lidell-Hart, and the Germans produced great theorists like Guderian and Rommel. In the U.S. the foremost tank specialist was Patton. The idea arose that tanks could be used independently of (rather than as an adjunct to), foot soldiers. By turning tanks "loose," they could be a highly "disruptive" force (in today's terminology), with mainly MOTORIZED infantry support..
The result was a new form of warfare known as the "Blitzkrieg" that was the antithesis of World War I tactics. But that arose only after 20+ years of thinking during an "interwar" period.
Broad answer for a broad question: the introduction of tanks shifted the advantage back in favour of the attacker.
During WWI, the machine gun made it very easy to defend a chunk of ground. You dug some trenches to protect against shells, set up this heavy weapon, and mowed down anyone who came too close. That's why they had such huge casualties for very small shifts in the battle lines.
Tanks were a way to get around that; the internal combustion engine let you move machine guns and cannons - and their crew, and armour for the crew - to where the enemy was. The full implications of that increased mobility were worked out in the interwar period, and led to the much faster and more far-ranging style of fighting in WWII.