Modern tellings of the Second Punic War are very reliant on ancient accounts; the two most important are the Histories of Polybius (Book III covers the origin of the war up through the battle of Cannae) and Livy's Ab Urbe Condita.

Polybius is a much earlier writer, having interviewed actual veterans of the Hannibalic War, and his account lacks many of the embellishments (anecdotes, heroics, and elaborate speeches) present in Livy's. While not perfect (Polybius was on very good terms with the Scipio clan, and there are definitely some extraordinary anecdotes), Polybius's account is generally quite plain and factual. Having some experience as a soldier, he had a great interest in military matters, so he covers the battles and campaigns of Hannibal quite well. The Histories are freely available online through multiple sites, so I'd recommend reading a sample of them before committing to buying a book.

Personally, I did not care for Richard A. Gabriel's strategic analysis in Hannibal: The Military Biography of Rome's Greatest Enemy. He reiterates the old claim that Hannibal's 'Hellenic' strategy forbade him from making a decisive attack on Rome after the victory at Cannae, and that he pursued a misguided strategy that put the subversion of Rome's alliances above the defeat of Rome itself. Putting aside the question of why this strategy would preclude an attack on Rome (after all, Polybius refers multiple times to the Carthaginians hoping to carry Rome itself by assault), I find logistical analysis much more interesting. Cannae is almost as far away from Rome as you can get in Italy, and it would have taken the better part of a month to cover the distance. Moreover, Hannibal still did not have a solid base of operations in Italy; his army controlled only the territory it was then camping on or marching over. Once they arrived at the walls of Rome and had to stay there, they quickly would exhaust local supplies, and would be unable to draw them from elsewhere until a secure base of operations was established.

That was a bit of a tangent, but really, 80% of what you need to know is in Polybius (and to a lesser extent Livy), with the rest being the contributions of modern archaeology and logistical analysis, such as Hannibal's Mules: The Logistical Limitations of Hannibal's Army and the Battle of Cannae, 216 B.C. by John F. Shean.

Livy has a couple that are decent. The language in them is a bit old, though. But seriously, find a solid translation of Ab Urbe Condita, books 21 through 30. I know of one which I cited below. There are also a number of decent narratives and history. Wikipedia is also a good way to begin your search for source books, if you look at the works cited at the bottom of the page.

Livy, Yardley, J.C., Hoyos, Dexter. Oxford World's Classics : Hannibal's War : Books 21-30. Oxford, GB: OUP Oxford, 2006.

I've replied below with the Livy source I have used, and the Polybius accounts are here, but both sources are fantastic reads. There are gaps in the Polybius accounts that the Livy text covers quite nicely. It is worth reading the Polybius account on the First Punic War, to see how the stage is set for the second...Livy's account of this is lost. Just a note of caution... Polybius tends to get carried away with long winded diatribes criticizing other authors on their historical accuracy or lack thereof, (I find this to be rather annoying) so consider yourself warned.