The central philosophy of Leninism, the theories outlined in The State and Revolution by Lenin himself, is actually a borrowed one. The core argument of the pamphlet is that Marx was basically correct about his ideas surrounding, you guessed it, the state of government and the need for revolution.
Regarding the state, Lenin discusses Marx and Engels and agrees with their conclusions that there is a caste-system in the governments of the earth. He goes further to state that in Russia, the state of the government was essentially corrupted socialism, where professional socialists had begun to work for the interests of a bourgeois elite class. The proletariat was the common people of Russia, of which there are many. The basic premise is that when the interests of the bourgeoisie are at the helm of the government, which Lenin argued was the case more or less everywhere on the earth, it becomes necessary to push the state towards absolute destruction by way of revolution.
When Marx discussed revolution, he talked of the eminent rise of the lower class, but Lenin changed that argument in his pamphlet. The way Lenin saw it, the efforts of communism were ideas worth spreading, and a citizen of the earth, Lenin wanted his Utopic vision to benefit everyone. Therefore the idea was born that Russian communism should be imposed first on its own public, and then on Europe. Lenin expresses an academic interest in a globalized communist Utopia.
This pamphlet is short, less than 100 pages, but it is dense with philosophies and speculations about the future of communism. These features here are the core ideas and the ones that came to shape the history of Russia, and also the history of the earth.