Is there a core of historical events from the Late Bronze Age in the description of the Trojan War, as conveyed by the sources, the Homeric Epics, and ancient Greek literature? If so, how could we separate this core from the poetic fictions by tracing the evidence found in archaeological testimonies? Can the archaeological testimonies from the then-known world, namely the findings and the texts of the archives that were read, from Hattusa, Egypt, and the Linear B tablets, provide us with information? Is there a relationship and connection between the findings from Cyprus and the Near East and the texts referring to Cyprus with the other evidence? Do these elements perhaps recall descriptions from ancient Greek literature? How many and when are the layers of destruction of Troy from the Late Bronze Age, which were brought to light by the archaeologists who excavated it, dated? How do these datings fit into the framework that emerges from the other archaeological findings? Did the Mycenaean Greeks of the Late Bronze Age possess the characteristics of a "great power," like the Kingdom of Hatti and Egypt, and when were they chronologically able to undertake a gigantic campaign against Troy? Given that - in all eras - countries possessing the characteristics of a "great power" - military strength, wealth accumulation, and economic power development - simultaneously proceeded with the construction of monumental large-scale works, developing the appropriate expertise and technology, did the Mycenaean Greeks possess these characteristics? What is documented by the archaeological testimonies? Are there records in the archaeological findings of campaigns by the Ahhiyawa/Achaeans or/and the Danaoi/Danaans against Hatti and Egypt, the two "superpowers" of the era?