What were the literacy rates among the general population? What about certain social classes, like the military or clergy? How were schools organized, public or private? What about universities? How widespread was access to education, especially in the more remote (Siberia) or non-Russian areas (Caucasus, Central Asia, etc.)
There are several questions here, so I will sketch out brief answers, but please follow up with any questions you would like me to go into greater detail!
Nicholas II did seek to modernize and standardize education in the late Empire, resulting in major increases in literacy, though you should consider the state of education in the 19th century: Russia had gone from a rural population composed of serfs and laborers to an increasingly urban, slowly industrializing economy. Nicholas did seek to increase literacy, but in a cautioned and often fractured way. These efforts were rewarded with something along the lines of 30-50% literacy [1, see a]. The census of 1897 gives literacy rates of 60% for the urban population and 43% for rural men and 22% for rural women; but over 95% in what would become Estonia [2]. The early start of these reforms comes between 1858 and 1864 under Alexander II, who instituted significant reforms including the eradication of serfdom. Following his assassination in 1881, Alexander III did seek to increase literacy and improve education as well, now drawing on the Church. Alexander III was quite reactionary due to the assassination of his predecessor, though by the 1870s Alexander II himself had become relatively conservative.
The second stage of reform comes in 1884 with the state support of parish schools, but their reception is a little muddled. Eklof argues that these are not that dissimilar from the zemtsvo schools and were efficacious. Certainly they did improve literacy, but the urban schools and zemstvos were invested in more than minimal literacy [3,4]. Clergy, on the other hand, would have long been literate, and in fact the children of clergy represent a large portion of University educated Russians in the 18th and early 19th centuries. One of the reasons these schools have a negative view around them is because of Alexander III’s reactionary goal in setting them up against perceived foreign influences, anarchism, and socialism. Nicholas II’s efforts were also closely aligned with the Church for these same reasons.
I spoke briefly about military literacy from 1881 to 1917 here. Eklof quotes that "it is stated to be a rare thing for a soldier to leave the army...without being able to read and write," (125) but it seems in practice, certainly by the 1880s, this wasn’t the case. And the literacy rate of 1897 for rural communities seems to corroborate this, as we would expect a higher literacy rate than was achieved if the service guaranteed literacy.
Universities are a difficult question given the extreme censorship of Nicholas I and Alexander III. The intellectual ferment of the 1830s and 1840s, and concurrent liberalizing movements, and never matched after Nicholas clamps down on teaching. In the 1860s, in fact, Saint Petersburg Imperial University was temporarily closed following student unrest. In 1905 Nicholas II restores some autonomy to Universities and they grow massively between 1864 and 1917, but this is still ultimately a small slice of Imperial Russian life, and were largely restricted to European Russia with a few exceptions, such as Tomsk. The Bolsheviks establish many universities early on, including Irkutsk and Yaroslavl . A recurring thread for Nicholas’ reforms, much like his predecessors, is “good, but…” and this is certainly seen in education.
As mentioned, a great reference work for rural education is Eklof’s Russian Peasant Schools (Berkeley, 1986). Grenoble focuses on the Soviet Union, in particular the approach to non-Russian languages spread across the empire (though she does touch on earlier education initiatives in these regions), while there are several good cursory overviews of Russian history that touch on literacy, education, urbanization, and radicalization between 1860 and 1917.
[1] Grenoble, Lenore. Language policy in the Soviet Union. Springer, 2003.
[2] Mironov, Boris N. "The Development of Literacy in Russia and the USSR from the Tenth to the Twentieth Centuries." History of Education Quarterly 31, no. 2 (1991): 229-52.
[3] Eklof, Ben. "The Myth of the Zemstvo School: The Sources of the Expansion of Rural Education in Imperial Russia: 1864–1914." History of Education Quarterly 24, no. 4 (1984): 561-584.
[4 ]Eklof, Ben. Russian Peasant Schools: Officialdom, Village Culture, and Popular Pedagogy, 1861-1914. University of California Press, 1986.
A) John Reed's Ten Days That Shook the World along with some later scholarship intimate a literacy rate closer to the upper levels here. Unsurprisingly, estimating literacy is quite difficult at this time, and as late as 1937/1939 the Soviet Union still struggled immensely with rural illiteracy, so I am inclined to think that the literacy rate was on the lower side of this range in 1900. See also Eklof, Ben. "Russian Literacy Campaigns 1861–1939." In National Literacy Campaigns and Movements, pp. 123-145. Routledge, 2017.
Unfortunately I don't have access to the book because I can't get into my library with the Coronavirus, but the book on this is Ben Eklof's Russian Peasant Schools. If you're genuinely interested in the topic I suggest you read that because, while it is quite long, it has almost everything you'd want to know!
I'll refrain from trying to remember the figures off the top of my head because I can't back it up with secondary source material, but you'll find that the late imperial period is when schooling for all classes of Russian society, especially peasants, really picked up.