This is a good, and, at times, an excellent introduction that delivers much more than just the battle of Salamis "the naval campaign that saved Greece". It is, in fact, more of a summary of the "Greco-Persian Wars" up to and including Salamis, to paraphrase the title of Peter Green's book, which started out as "the Year of Salamis" when it was first published in 1971. Surprisingly, this major book on the subject is not even referenced in the bibliography, although Tom Holland's bestseller ("Persian Fire"), which happens to be largely a rework of Peter Green's book, is listed, alongside Barry Strauss' must more serious book on Salamis.
The first part, called "Origins of the Campaign", describes in fact the origins of the war, going back to the conquest of Lydia and the Ionian Greeks by Cyrus in 546 BC. This turns out to be one of the book's strengths because it allows the author to provide a lot of context. It also allows him to paint a much more realistic portrait of the Persians and their Empire and present what has, since the early 1990s, become the modern view. Contrary to all of the propaganda developed by the Greeks and relayed by at least some historians in the past, the Persian Empire was the superpower of the time. It was certainly not decadent, neither were the Persians and their subjects effeminate and soft. Moreover, as the book also explains very well despite its limited size, the Ionian Greeks, supposedly groaning under the Persian oppression and presented as "slaves" by Herodotus, seem to have been rather prosperous before their revolt. On the other hand, and following in the footsteps of Peter Green who was one of the first to emphasize this point some 40 years ago, the book also makes clear that about 30 cities in Greece out of at least several hundred actually fought against the invaders. The Macedonians, the Thessalians and the Thebans (and many others) sided with the invaders whereas the Argives remained "neutral" and were ready to join the Persians if only because Sparta was on the other side. So William Shepherd is perfectly correct to emphasize that Greek cities, despite their shared identity, spent more times warring against each other, and may even have preferred siding with third parties against their hated neighbour city.
One point which he did not perhaps emphasize is that there were political rivalries and power plays between various factions, all of which were headed by aristocrats, even the ones that were backed by the less wealthy citizens. This included both Athens and Sparta and, in both cases, some of the "losers" could and did seek refuge within the Persian Empire. Although he does not insist on this particular point (the cities were divided within and between themselves), the author does, however, a good job in showing that Marathon was, from the Persians viewpoint, a minor setback and Thermopylae a costly victory, but a victory all the same. The parallel drawn with more recent events when mentioning the storming of the Athens' acropolis ("Mission accomplished") is somewhat superficial. While Xerxes certainly did send a triumphant despatch back to Susa announcing that Athens was duly chastised and punished, he knew perfectly well that this was not "game over" on sea or on land. As the author clearly shows, the Persian King of Kings was well aware of the need to defeat the allied fleet before assaulting the Isthmus and refused a plan suggesting to bypass it. Contrary to what the author claims (page 41) in a rather sweeping statement, the decision not to pursue this course was not "a fatal failure of vision and nerve". It was tactically and strategically a sound and prudent decision, especially after Artemission. The chronology also contains a little typo. As the text makes clear twice throughout the book, Xerxes was assassinated in 465 BC, the year after the defeat of the Eurymedon and not, as indicated by mistake in the chronology, in 455 BC.
The initial size of the Persian fleet, its losses during the two-year campaign and its size at Salamis have been discussed by historians for decades. In this book, the author has chosen to dismiss the huge losses mentioned by Herodotus because of bad weather (some 600 triremes) as a wild exaggeration and reduce by about the third the initial number of 1207 that is mentioned, considering that this is more probably the grand total for the whole of the Persian Empire. While the first point is very probably correct - it is somewhat rare for a fleet to be entirely destroyed in a storm and even rarer for this to happen twice in a few months - the second point is no more than a guess. It also does not account for the two bridges across the Hellespont that the Persians built. If these were pontoon bridges made with ships tied together, several hundred ships would have been needed for each of them.
The description of the battle itself is great.
The plates, maps and diagrams are very helpful in understanding what happened, especially since both Herodotus and Aeschyle, our two main sources and the ones closest to the event, tend to describe the battle from the viewpoint of individual participants rather than providing us with the "full picture". The explanation regarding to role of the Corinthians and what was probably a feigned flight is particularly interesting, since they came back to attack the Phoenician squadron either in the flank or in the rear. A minor omission is the absence of any discussion of two episodes, one before and one at the end at the battle, that Herodotus reports at length and uses to emphasize the role of Aristides, one of the leaders of the aristocratic and conservative faction and the faction from which Herodotus seems to have obtained most of his (somewhat slanted and anti-Themistocles) information.
Then there are a couple of technical points which are somewhat questionable. The author mentions at one point when describing a "Greek" trireme, based on the reconstruction of the Olympias, that he is essentially describing an Athenian trireme as it was around the beginning of the Peloponnesian War, some fifty years later. He mentions that both the ships and their hoplite complement may have been somewhat different at the time of Salamis, with more than what became the standard complement of 10 hoplites and 4 archers in the heydays of the Athenian navy. Despite this, when describing the battle itself further on in the book, he essentially assumes that this was the complement on all the Greek ships at Salamis, which is rather implausible. The battle was to be fought in the narrow straits where swift manoeuvring was less important than boarding. The Persians had at least 40 fighting men per ship and the Allies had several thousand hoplites in addition to the complement of 10. It is somewhat difficult to believe that they would have chosen to be deliberately outnumbered three to one when fighting each boarding action when they had the means to at least minimize this disadvantage.
A related point is the author's statement, backed by the plates that the hoplites on board were unarmoured in order to avoid hindering their movements and drowning if they fell overboard. This is also implausible. While they would be unlikely to wear metal armour for the reasons mentioned above, they would still very much need some protection against the superior archery of the Persians. They could therefore very well have worn leather cuirasses which would have offered the most logical compromise between these various constraints.
Because of the glitches, this book is worth four stars, but not five. It is, however, an excellent introduction to the battle of Salamis and to the Greco-Persian wars, more generally, although it is a pity that the author did not see fit to include Peter Green in his sources, something that would have completed his bibliography.