Kostrov was educated in the Slavic Greek Latin Academy and received an annual pension from the Moscow University for odes and other poems he would write for special occasions.
[2] Intent on continuing his education, Kostrov composed a request in verse to his relative Archimandrite Ioann Cherepanov, who was a member of the synod and a former student and teacher at the Vyatka seminary.
Kostrov's appeal was successful, and he was able to attend, albeit unofficially, the Slavic Greek Latin Academy in Moscow, the highest ecclesiastical school in Russia.
Archbishop Platon of Moscow, the director of the academy, supported the petition and described Kostrov as an honest and successful student with a gift for theology.
A contemporary, Mikhail Dmitriyev, described Kostrov as "not very tall, a tiny little head, somewhat snub-nosed, his hair smoothed back, bent at the knees, not too steady on his feet."
According to Altshuller, traces of the influence of Homer, Ossian and biblical poetry in Kostrov's odes display his awareness of the early Romantic approaches.
While attempting to escape from classicist conventions, he decided to translate the Greek epic into Alexandrine verse (iambic hexameter, with rhymed couplets), the standard meter for heroic subjects in French classicism.
In Altshuller's view, Kostrov's choice of meter "doomed Homer's epic to serious distortion, imbuing it with the spirit not of antiquity but of classicism."
Despite this, Kostrov, with his adeptness in philology and ancient languages, made an effort to recreate the simplicity of the epic and not force it to correspond to classicist tastes.
In this striving for authenticity and his use of archaic and Old Church Slavonic words to reflect the ancientness of the work, Kostrov moved in the direction of the Romantic ideas of national art.
Empress Catherine had designs on Ottoman territory and considered plans for the creation of a Greek state centered in Constantinople and ruled by her grandson.
The publication of Kostrov's Iliad includes a dedication in verse to the empress, in which he compares her to Athena and foresees the liberation of the Greeks by Russian armies.
His translations of the seventh, eighth and part of the ninth books were discovered after his death and published in the journal Vestnik Yevropy in 1811.
Kostrov's translation of Ossian, made from a French version by Pierre Le Tourneur, was published in two volumes in 1792 under the title Galskie stikhotvoreniya (Gaelic poems).
At the age of fifteen, Alexander Pushkin wrote a poem in which he mentioned Kostrov together with Luís de Camões, the Portuguese epic poet who likewise died in abject poverty.
A simple-hearted man, gentle, talented, and completely indifferent to money, Kostrov was received by his contemporaries and immediate descendants as the embodiment of the romantic, unsettled, solitary poet.