Leo and Sofya's mother were childhood friends. After meeting with Sofya's family several times, he decided to propose to Sofya through a letter. Leo decided if her sister Tanya sang the last high note of a song well, it was a sign from God to not wait to propose. Tanya sang well and Leo gave Sofya the letter on September 16, 1862.

Leo: “Sofya Andreyevna, the situation has become intolerable to me. Every day for three weeks I have sworn to myself: today I shall speak; and every day I leave you with the same anguish, the same regret, the same terror, the same joy in my heart ... I am bringing this letter with me, to give to you in case I lack the opportunity, or the courage to speak ... Tell me, tell me truthfully, do you want to be my wife? But do not answer yes unless you can do so fearlessly, from the bottom of your heart. If you cannot, if you have the shadow of a doubt, then it is better to answer no. For the love of God, be certain! If you say no, it will be awful for me, but I am expecting it and shall find strength to bear it. For if I were your husband and were not loved as much as I love, it would be more awful still.”
Source: Henri Troyat. Tolstoy. pg. 245.
"Before the wedding, he [Leo] asks her [Sofya] to read his personal diaries. She is devastated but forgiving. Many details of their courtship appear in Levin and Kitty's romance in Anna Karenina."
Source: "A Tolstoy Timeline." PBS.org.

Sofya and Leo were married a week later.

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Quotes About Marriage and About the Marriage of Sofya and Leo Tolstoy

Sofya and Leo Tolstoy Marriage Profile