Although India, and Russia share a long history of cultural and intellectual exchange, history of instruction of Russian as a foreign language in India is not that old. The formal instruction of Russian language was first started in early 1940s at Calcutta University at Kolkata (West Bengal, India). It was taught as a part time course by Madam Buseva. Later in 1946, Delhi University started offering Russian Language courses, followed by University of Allahabad in 1948. In 1965, establishment of Russian Culture Centre and the Russian Research Centre at the Jawaharlal Nehru University paved the way for a systematic study of Russian language in India. In the 21st century, Russian is taught at several universities and institutions spread across India.
Russian language textbooks printed in India are not many, and most which are available use English as a medium of instruction. This creates further challenges for Indian learners in terms of speaking and listening skills in Russian. In 1958, Foreign Languages Publishing House (Russian: Издательство иностранной литературы) published the Hindi translation of ”Russian : Textbook of the Russian Language for English Speaking People, Part 1 (1946)” written by Nina Potapova. Later in 1960 the 2nd part of the same book was published. You can read these books via these links
In 1997, Government of India published the booklet हिन्दी रूसी वार्तालाप पुस्तिका hindī rūsī vārtālāp pustikā for learning Russian through Hindi medium. In 2006, Prof. Hem Chandra Pande revised it. He taught Russian language at my alma mater (JNU, India) for many years.
You can download this book using this link