Ultimately: Communism. A classless, stateless (as the state is an institution of class rule) society that encompasses the whole world. Productive capacity has advanced to stage when little work is required. People are free to follow what pursuits they want.
In order to get there: Overthrow the 'Dictatorship of the bourgeoisie' and replace it with 'dictatorship of the proletariat'. This means a class dictatorship, not what the word dictatorship usually means. This means there would still be democracy among the vanguard and/or working class (depending on situation, the whole working class is unrealistic when most of them are being wiped out by counter-revolutionary war aided by the UK, US, Japan, France and others).
Where did it go wrong then? The working class was mostly destroyed in the civil war. This led to a situation where the party had nothing to hold check on it, and a thermidor could emerge. For a more indepth analysis read Trotsky's The Revolution Betrayed on Marxists.org and The Degenerated Revolution on FifthInternational.org
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Stalin had always supported the Bolsheviks, while Trotsky only switched from the Menshevik party to the Bolshevik party after it was apparent that the Bolsheviks would win. Trotsky was a thinker with brilliant speeches, Stalin used force for votes. Trotsky led the army, while Stalin was the secretary. Stalin had great political appeal, but Trotsky had great militaristic and organisational appeal. Furthermore, Stalin was mentally and physically strong, but after Lenin's death, Trotsky began breaking down. The power struggle between the two sparked a conflict in which Trotsky fled the USSR but was later disposed.
Leon Trotsky.
He drove Trotsky out by a police force that he created in secret. Then, i think he killed Trotsky or sent him into exile.
Stalin, Trotsky and Lenin.
Vladimir Lenin and Leon Trotsky were both editors of the Iskra in Russian 1902. Lenin and Trotsky were also both Russian revolutionaries, even though they did not see eye to all on all things related to this. However, in 1904 the men reconciled their differences.