How did Russia become a European power before World War 1?
Russia, whether as Kievan Rus or Muscovy, has always been a
power in Eastern Europe. Soon after the fall of Byzantium, the
Princes of Muscovy claimed to be the true successors to the eastern
part of the Roman Empire and adopted the Byzantine double-headed
eagle as their dynastic 'beast'. (That's why the Romanovs also used
it). Muscovy claimed to be the protector of Orthodox Christianity
and also claimed the right to intervene at will in the Balkans.
Until about 1780 most of this was just talk. From about 1650
onwards Muscovy/Russia began to push westwards into Poland. War
with Sweden in 1700-21 brought further westward expansion. Tsar
Peter the Great (reigned as sole Tsar 1696-1725) and later, also
Catherine the Great (reigned 1762-96), made huge efforts to
'westernize' Russia in the 1700s. Russia became involved in many of
the major European wars from the Seven Years' War (1756-63)
onwards. So Russia was a major European power long before the
approach to WW1.