Great Battles, subtitle "decisive" makes me think about the selection of battles based on the extent of decisiveness. Surely that word must refer to the degree to which the conflict brought a large-scale, pivotal and irrevocable change in regional or global history?
"Great" on the other hand could simply refer to the scale of fighting (usually representative of a large-scale war), skill of one or more commanders, or the passing of the battle into the folklore of one of the participants. These are not necessarily decisive. A middle ground is those that saw a significant change in military technology or tactics that were then adopted widely. A fourth category was ones that symbolic - inevitable but marking the end of an era.
So decisive: I would suggest Manzikert, Ain Jalut, first battle of Panipat, Bouvines, fall of Tenochtitlan. Possibly Kosovo (1389), Sedan (possibly).
Marathon - no - great only in the sense of folklore. Salamis - yes. Gaugamela - not sure. Canne - no (see below), Alesia - yes, Adrianople - yes. Tours - for sure, Hastings yes (as it moved England into France's orbit and set the trend for 700 years), Tannenberg - not sure.
Hattin I would remove as, to me, it was inevitable that the crusade states would fall (long supply lines etc). Agincourt because it did not turn the course of the war (which the larger country won) but simply passed into the forelore of one of the protaganists. Constantinople (symbolic only). Lepanto - yes. Armada - probably yes, although the Spanish plan was so complex and brittle it was unlikely to succeed. Lutzen (hard to argue this was decisive in the 30 Year War and besides was this really a decisive war, or simply horrific and long?).
Blenheim clearly qualifies on the skilful category and perhaps decisive if it ended Louis XVI plans for hegemony (not sure as the war carried on for another 9 or 10 years). Saratoga is a yes.
Austerlitz I would remove and replace with Leipzig. Waterloo not sure. The problem with Napoleon's victories is they were skilful and to some extent influential but ultimately he lost the war. The same argument applies to Hannibal
Not sure about the American Civil War. To me, the key one would be the one that committed the North to the full defeat of the South, rather than a compromise. Once committed and with suitable military leadership (the lack of which dogged them in the early year or so), it was inevitable they would prevail because of the comparative scale of industrial output and available manpower.
First world war - the decisive battles were First Marne, Jutland (in a strange way) and Amiens / 100 Days. Somme and Verdun were representative but not decisive.
Second world war - hard to argue against the inclusion of Stalingrad and Midway (incredibly decisive), but I am not sure about Battle of Britain. Possibly a greater argument for the Battle of France because this tipped Hitler's self-confidence into hubris.
Not sure about the Tet offensive as don't know about it but Iraqi Freedom is a clear "no chance" on any category!
This book got me thinking and I would like to thank Christer Jorgensen and his team. Two minor points - one or two of the numbers were doubtful (such as the number of Swedes who landed with Gustavus A in 1630) and left and right were muddled up when referring to the battlefield in a few cases I think.