Crossing the Alps
In 218 BC Hannibal led a great army, including dozens of war elephants, from Spain across Gaul and over the perpetually snowbound, treacherous Alps, suffering terrible losses on the way from the bitter cold, landslides, and attacks by local tribes, so that only about half his force reached the plains of northern Italy — one of the boldest strategic maneuvers in ancient military history, utterly shattering the Roman strategic expectation that "the Italian mainland was impregnable."
The Battle of Cannae: A Classic Case of Double Envelopment
In 216 BC at Cannae Hannibal, with a force far inferior in number to the Roman army, used the tactic of deliberately withdrawing at the center to draw the enemy deep in, then encircling with his elite cavalry from both flanks, annihilating nearly seventy thousand Roman troops — the Roman dead in this battle exceeded the total dead of the later Battle of Gettysburg in the American Civil War; this "Battle of Cannae" has for over two thousand years remained the most classic historical case taught in military academies worldwide on the tactic of "encirclement and annihilation."