There have been many styles of architecture throughout Russian history because at various point, depending on who was in charge of the country/empire/etc., Russian architecture was inspired by western culture and at other times it focused on russificaiton.
Examples of these various architecture styles:
The Intercession Cathedral (aka Cathedral of St. Basil the Blessed) built 1555-61
The Church of the Icon of Our Lady of Kazan
Peter's Palace in St. Petersburg
From the 1760s the Winter Palace was the main residence of the Russian Tzars.