After graduating from the Konstantinovsky Land-Surveying Institute (Russian: Константиновский Межевой Институт) in Moscow, Letnikov attended classes at Moscow University and the Sorbonne.
He obtained the degrees of Master and Ph.D. from Moscow University in 1868 and 1874 respectively.
From 1883 he was the principal of the Aleksandrov Commercial School (Russian: Александровское коммерческое училище, currently The State University of Management)[1] and from 1884 he was a Corresponding Member of the Russian Academy of Sciences.
His most renowned contribution to mathematics was the creation of the Grünwald–Letnikov derivative.
Letnikov died in Moscow in 1888 and was buried in the cemetery of the Novo-Alekseyevsky Monastery.