Born Pinches Borutsch (Russian: Пи́нхус Бо́рух) in Potscheff near Chernigov and raised to Shklov, a small provincial town in (currently Belarus) and Mogilev, the biggest town of the three in the Russian Empire (currently Belarus), Axelrod was the son of a Jewish innkeeper.
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In the mid-1880s Axelrod established his own small company producing kefir. By the end of the 1890s, Axelrod's company had offices in Zurich, Geneva, and Basel, which provided steady income and allowed him to support revolutionaries. In 1908, Axelrod sold his company in exchange for the retirement payments to him from the new owner.

Influenced by Mikhail Bakunin in his youth, he remained an Idealist even after adopting the Marxist philosophy of historical materialism. Axelrod co-founded the Marxist group Emancipation of Labor in Switzerland with his lifelong friend Georgi Plekhanov and Vera Zasulich in 1883. In 1900, Axelrod, Plekhanov and Zasulich joined forces with younger revolutionary Marxists Julius Martov, Vladimir Lenin and Alexander Potresov and the six edited Iskra, a Marxist newspaper, from 1900 to 1903. When Iskra supporters split at the Second Congress of the Russian Social Democratic Labor Party in 1903, Axelrod sided with the Menshevik faction against Vladimir Lenin's Bolsheviks.

In 1917, after the February Revolution Axelrod returned to Russia. By then some Mensheviks had already joined Kerensky's Provisional Government and supported government war policy. Despite all his efforts Axelrod failed to gain Mensheviks' support for a policy of immediate peace negotiations with the Central Powers. After the Bolshevik victory, which Axelrod called a "historical crime without parallel in modern history", he toured the world rallying socialist opposition to the Bolsheviks.

Axelrod died in exile in Berlin in 1928.

Wikipedia wrote:Axelrod grew up in Stuyvesant Town on the East Side of Manhattan, NY. He is the son of Myril Bennett, a journalist at PM, a left-wing 1940s newspaper, and Joseph Axelrod, a psychologist and avid baseball fan.