Short answers, pulled from the story.
Imperialism is the maintaining and extending of power over foreign nations through expansionism, using both hard power, meaning military and economic force, and soft power, meaning diplomatic and cultural influence. Hannah Arendt and Joseph Schumpeter defined it as expansion for the sake of expansion, while it focuses on establishing or maintaining hegemony and a more formal empire.
The word imperialism derives from the Latin imperium, meaning to command, to be sovereign, or to rule. It was coined in the 19th century to describe Napoleon III's attempts to gain political support by invasion, was applied to the British Empire during the 1870s, and had acquired a positive connotation in the West by the 1880s.
Edward Said held that imperialism is the practice, theory, and attitudes of a dominating metropolitan center ruling a distant territory, while colonialism refers to settlements on a distant territory. Young added that imperialism implements state policy while colonialism may reflect commercial intentions supported by force.
The Age of Imperialism refers to the period that pre-dates World War I, ending commonly at 1914, with a starting date that historians place anywhere between 1760 and 1870. The later date makes it identical with the New Imperialism, and the era included the Scramble for Africa and the Great Game.
John A. Hobson argued in Imperialism: A Study in 1902 that financing overseas empires drained money needed at home and put a lid on domestic wages. Vladimir Lenin built on this in Imperialism, the Highest Stage of Capitalism in 1916, portraying imperialism as monopoly capitalism on a global stage and explaining the world wars as battles between imperialists for external markets.
Since the 2010s Russia under Vladimir Putin has been described as neo-imperialist for occupying parts of neighboring countries, including the 2008 invasion of Georgia, the 2014 annexation of Crimea, and the 2022 invasion of Ukraine. Four months into the Ukraine invasion, Putin compared himself to Peter the Great and spoke of returning Russian land to the empire.