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Thucydides' history of the Peloponnesian war between Sparta and Athens, of which he was a contemporary and participating general, is studied still today in war academies and by political scientists for its timeless insights and hypotheses about strategies and the causes and nature of war.

Has Thucydides been continually studied since then (5th century BC)? Did he influence the later Theban war with Sparta, and Alexander the Great? Did Roman generals and politicians read him? Was he well known in medieval Europe? Did famous later commanders like Frederick the Great and Napoleon read Thucydides? When did he reach outside of Europe and the Mediterranean? During what periods and in which regions has he been influential (today he seems to be mandatory reading throughout the world)?

Thucydides has been widely read and cited since ancient times, though not always to same extent in different periods. Martin Hammond, in his translation of The Peloponnesian War, observes:

Thucydides was not as widely read in the fourth century and the
hellenistic period as the more obviously attractive Herodotus and
Xenophon, but he was far from being totally neglected, and knowledge
of him can be found in fourth-century orators and philosophers as well
as in historians. One remarkable example is the use by
Aeneas Tacticus, in his work on withstanding sieges, written in the
mid-fourth century, not only of Thucydides’ account of the Theban
attack on Plataea in 431 but also of Brasidas’ speech before the battle
of Amphipolis.

Among Romans and, later, Byzantines:

By the first century bc his history was well known in Rome. Lucretius
ended his De Rerum Natura with an account of the plague at Athens.
Cicero commented on Thucydides’ history, not recommending it as a
model for Roman orators to follow, and seems to have relied on it for
his knowledge of fifth-century Athenian oratory. The historian
Sallust took Thucydides as a model (inter alia, for the debate between
Cato and Caesar on the Catilinarians following the debate between
Cleon and Diodotus on Mytilene65), and his indebtedness to Thucydides
was remarked on by Livy and others. Dionysius of Halicarnassus,
active in the time of Augustus, wrote essays About Thucydides and
About the Distinctive Features of Thucydides. Quintilian in the first
century AD commented on Thucydides’ style. Lucian in the second
century, in his essay on How to Write History, described Thucydides as
‘the man who legislated for history’. Much later, in the Byzantine
empire, Procopius, the historian of Justinian, was an imitator of
Thucydides, and the plague at Athens was pressed into service again
when he wrote about the bubonic plague in Constantinople in 542 – 3.

Livy's account of the Second Punic War starts with

a direct echo of Thucydides' assertion of the importance of his
subject, complete down to the larger reasons given in support of the
claim, but differing in particulars and in the background material.
Other passages, too, in Books 21-30 point to Thucydides' influence,...

Also, Plutarch reports that Cato the Elder "profited" from Thucydides, probably when writing Origines (now lost).

With few people in the Middle Ages being able to read Greek, Thucydides' influence waned until Lorenzo Valla made the first complete Latin translation in 1452. Before that, though, the Grand Master of the Knights Hospitaller Juan Fernández de Heredia (c.1310 to 1396) translated parts of Thucydides' work into Aragonese.

Later,

realists, such as Machiavelli and Hobbes, agree with Thucydides that
"might makes right" is an intoxicating precept for states to indulge
in.

Not everyone would agree that there is "much trace of the influence of
Thucydides in Niccolò Machiavelli" (e.g. Hammond), but

A landmark in the development of a scholarly approach to Thucydides,
as opposed to the use of him as a model, came with the editions of
Henri Estienne (Stephanus), first published in 1564 and revised in
1588.

Many 19th century historians and philosophers read, cited and / or were influenced by Thucydides, Macauley and Nietzsche among them, as did Napoleon.

In the American Civil War,

Basil Lanneau Gildersleeve, the first great American classicist, spent his summer vacations campaigning with Robert E. Lee’s army...
When he wrote about his experiences more than thirty years later, he
playfully entitled the piece “A Southerner in the Peloponnesian War.”