Defeat by Rome in the first Punic war (264−241) had nevertheless left a Carthaginian political and military presence in Iberia. Hannibal’s father Hamilcar and brother-in-law Hasdrubal commanded there in turn, and were succeeded after their premature deaths by Hannibal. He attacked the Rome-friendly city of Saguntum, and the outbreak of the second Punic war followed. Its much-disputed causes are addressed. Hannibal wrong-footed the Romans by crossing the Pyrenees and Alps with elephants and descending into Italy. By brilliant tactics, he won four battles in rapid succession (218−216) and increasing order of scale and gravity: at the Ticinus and Trebia in north Italy, then an ambush at Lake Trasimene in Etruria, and finally the massive victory at Cannae. But he rejected his lieutenant Maharbal’s advice to march on Rome. Appendix 3.1 argues that Hannibal became increasingly isolated after these successes, and Appendix 3.2 that there was only one Maharbal.