Very nice overview. Written in clear, short declarative sentences. It presents various interpretations of the existing archeological and historical evidence and the author's view on the subject but the author never flat out dismisses contrasting views.
For those unfamiliar with the subject, roughly 700 or so years before classical Greece, that is about 1200 B.C. There was an extensive network of civilizations and empires in the area from Greece, the eastern Mediterranean, Asia Minor, Egypt, and Mesopotamia. This was called the Bronze Age. Something happened and it all fell apart. Bronze depended on imported copper and tin from far away areas. After the collapse, iron was used, because it is relatively common everywhere and no long distance trade was needed. We think iron is an advance, but early cast iron was inferior to cast bronze. Only the later development of forged steel was an improvement. So with the social collapse, trade collapsed, technology collapse, writing disappeared most places and there was a period of dark ages similar to that after the collapse of the Roman Empire. During this transition things like the Trojan war and Exodus and the founding of Israel occurred. It is a very interesting period and the book covers it well. ( )

The book would have deserved a better editor: there are lots of typos (one systematic - Robbins appears to believe that "martial" is spelt "marshal"), and some statements that are just odd (such as Assyria falling a "short time" after 722 BC - well, maybe if you're a geologist). Also, there are no footnotes, which is a shame.

Robbins goes through (and criticizes) a great many alternative hypotheses, and frequently stresses uncertainty and ambiguity, but his basic synthesis may be summarized like this: Mycenaean Greece and Hittite Anatolia were brought low by famine and/or epidemic disease, and out of the chaos "Sea People" groups, primarily from southern Anatolia and northern Syria, go south to trouble Egypt and, as the Philistines, settle in Palestine. He spends a lot of words arguing against any of the "Sea Peoples" being of Greek origin, and emphasizing that the Dorian takeover of the (bulk of the) Peloponnese and the Arcado-Cypriote of Cyprus may have been into lands already depopulated by prior collapse. One gets the impression he's overreacting to scholars who have tended to see Greek agency in everything. On the other hand, he is inclined to grant a historical basis to the Trojan War.

He also devotes a couple chapters to the origin of Israel, ending up prefering a somewhat "maximalist" account granting a historical kernel of truth to the Exodus. He appears to take the historicity of David and Solomon as a given, which surprised me a little.

Philological issues are, naturally, frequently touched upon, but the treatment often consists merely of noting that one unnamed scholar concludes this, another one equally unnamed concludes that, therefore the issue is unresolved. Fair enough if one doesn't have the expertise to make one's own judgments, but still a bit disappointing, and the arguments that are presented often seem a bit weak or elliptical.

Discussing the end of Mycenean Greece and the apparent accompanying depopulation, Robbins suggests epidemic disease (or Plague, as he puts it, complete with capital) as a major cause. To bolster this, he brings up the Black Death, but I don't think the comparison helps his argument - disruptive as the Black Death was, it didn't topple any kingdoms, cause major cities to be abandoned, or bring about an end to writing. Somewhat similarly, arguing that famine did in the Hittite empire, he refers to frequent droughts in 20th century Turkey, and notes that climate probably hasn't changed much since the Bronze Age. The problem being, of course, that Turkey didn't implode in the '30s (the example discussed), and if climate was similar in the Bronze Age, similar famines must have been repeatedly experienced and survived by the Hittites. If a drought-induced famine finally did topple them, either it must have been an infrequent, unusual and particularly severe drought (as the ones in the '30s apparently were not), or some other condition must have made them too weak to resist what would be normally survivable - but then it doesn't seem very sensible to consider the drought the primary cause of the collapse.

In summary, there's a lot of interesting stuff here, and Robbins seems fair and even-handed enough in presenting opposing viewpoints, but I'm less than fully convinced of many of the conclusions.