Kiselyov attended the district school in Mtsensk and later enrolled at the Gymnasium in Oryol, the main city in the region.

He graduated from the Gymnasium in 1871 with the gold medal and, in the same year, entered the Physics and Mathematics Faculty of St Petersburg University.

In 1875, Kiselyov graduated from the university with a degree that allowed him to teach in a Gymnasium.

Kiselyov himself suggested that the properties required of a good textbook were precision, simplicity, and conciseness.

In the early 2000s these three titles were re-issued primarily to acquaint teachers of secondary schools with the style of mathematics education employed a century ago.