Hannibal the Great Tactician
Hannibal is considered one of the greatest strategists of all-time. He was an innovator and modernized war-fare. He was a genius and also had common sense. These two are a potent combination. He was successful not only because of his battle tactics but because of the strategies for his military outside of battle as well.
War-fare in that point in history was fought with infantry in a phalanx formation of multiple rows of men. This wasted the amount of men who could fight at one time and caused the army to be less effective. Four to six rows would be ideal but because armies back then were mostly of citizens (not real soldiers) they would die to quickly requiring you to have many rows of men to reinforce the lines.
When Hannibal came to power he changed war-fare in three major ways:
1) He had one of the first professional armies. His men were trained and battle-hardened. This allowed him to have between four to six rows of men.
2) Because he freed up so many of his men he was able to use them at parts in the battle where the line needed to be reinforced. This is called a reserve.
3) He did not lead on the front line so he was able to effectively command the battle.
A more comprehensive explanation of why he was so successful can be found here.
The Envelopment Tactic:
The tactic Hannibal used during the Battle of Cannae was an envelopment tactic (The Pincer Movement). Hannibal's least effective infantry were placed in center of the line while his best units were placed on the outside of the line. As the Romans began to push back the weaker mid part of the line, the outside infantry pushed back the Romans outside section of the line. This allowed the bulk of the Roman army enter into the center of Hannibal's forces. The Romans became encircled in a half moon shape as a result. All of this was done while Hannibal's cavalry was fighting the Roman cavalry. When the cavalry defeated the Roman cavalry they would close in the backside of the moon shape and completely destroy the Roman army. Other militaries have since used this tactic. Shaka Zulu had a strategy called the "bull horn" which was very similar.
The greatest attribute to Hannibal's success was his effective use of well trained cavalry. This factor alone has been the deciding factor for many of his battles. Each of the four battles mentioned before have been won due to cavalry. His brother Mago and Maharbal were his chief cavalry leaders.
If you are interested in war strategies and such this covers the basics as well as advance. Here!