A classic - look it even says so -
a portion of Livy's History of Rome. Not being a scholar I forget the exact details but much of this is sourced to the lost works of Polybius; and the introduction and various footnotes are somewhat sniffy about Livy's qualities; but I'll take it all as read. Much like Thucydides he has at suitable moments inserted speeches from the generals, or the senate, and it seems like that these are "what he felt should have been said at that point" rather than actual verbatim reports.
As well as the actual battle reports he tells us every year about the election of the new consuls, and aediles, and so on; which the Romans faithfully did all throughout the war; and how they got their commands - via decision in the Senate, or by lot, or by agreement - and this all gives the impression of a well-ordered republic that even at times of stress, when the rules needed to be adapted, it was all done according to rules. We don't see this from the Carthaginian side. Oh, and they took their signs-and-portents very seriously.
The history is very much one of battles, with a few notes about one side or another ravaging the countryside, and sometimes being short of grain. But what one sees is both sides constantly raising fresh troops, although I get a slight impression that the Romans are more raising their own, whereas the Carthaginians are raising Spanish and Gauls and Numidians and so on. So my suspicion is that the Roman state was just bigger, and more productive, and that an economic history would make this much clearer. Somewhat in the way that economics, and the vast USAnian productivity, would tell you that the USA was going to win the Pacific war in WWII without actually having to look at the details. Livy always counts armies by total number of troops, foot and horse separately. Sometimes he notes that some were raw troops, or peasants pressed into service. But usually he just goes by numbers. I'm curious if the commanders thought that way, too. But they must have been aware that veteran well-armed-and-armoured legionnaires would destroy many times their number of peasants.
So the story goes: Hannibal, starting in Spain, with a lust for glory (Livy lavishes praise upon Hannibal's qualities as a general - possibly in part to excuse Roman failures - but calls him cruel, treacherous and faithless as a person), attacks a random Roman city in Spain then crosses the Alps with great hardship into Italy. Note that he doesn't do this as a surprise attack - the Romans are fully aware he has crossed, though not his exact track - but, oddly, as the easiest way to get there. I completely don't understand why he didn't go by ship. Anyway: once there, he decisively defeats several Roman armies and may have been only a short hesitation away from taking Rome itself. But he does hesitate, and after that, even though he wanders around Italy for years - indeed, more than a decade - variously taking and losing cities and battles and ending up for no obvious reason all the way down in Bruttium, he seems to become largely irrelevant. He isn't the only Carth general - there's Mago, and more than one Hasdrubal - but as the title hints, he is the main one, in a way that isn't matched on the Roman side.
I thought that "Hannibal crosses the Alps" was most of the story but no: that is only chapter one. In subsequent chapters - the book is arranged by years, this is convenient as the Roman commanders change with the years - we go back to the war in Spain, which ebbs and flows, with Roman consul-lead armies getting destroyed and re-created, and in the end Scipio Africanus-to-be comes in and kicks the Carthaginians out. As a sub plot there's action in the East too, with Philip being encouraged to cause trouble by the Carths, but all that generally seems to fizzle out. And then in the end, Scipio crosses to Africa - which finally pulls Hannibal out of Italy, since they now need him to save Carthage - and wins. This BTW is the second not the third Punic war, so Carthage is merely captured, not destroyed, and peace is made.
Speaking of peace: a strong lesson from all this - and it's the same from the Peloponesian war - is that the side that is winning never wants to make peace. At various points the Romans are on the ropes, and so at that point the Carths are all gungo-ho; and then later the Carths sue for peace - and actually the Romans give them an armistice, but it breaks down, and the Romans crush them. Although individuals on either side have enough foresight to say "we're doing well now, let's not risk everything, we should agree to peace", the weight of opinion always overrides these sane voices.
In terms of war, the lesson - also hammered home in Ceasar's stuff - is that poor generals can get a lot of people killed. "poor" usually means rash, or careless; but it sometimes means over-cautious.
Life was pretty grim back then, and I suspect most of the soldiering took place under circumstances that we would nowadays consider intolerable, much like Sherman's marches in the US civil war. Livy reports with little comment that, when cities were captured, any Roman deserters captured were crucified. So lots of other stuff we'd consider terrible probably isn't even mentioned.
Part three of the Helliconia trilogy by Brian Aldiss; now re-read after an interval of decades. I like it; it is well written and has a sweep and grandeur that most other books lack; the characters are real people.
I wanted to get a towbar, 
