Trotskyism is the theory of Communism as advocated by Leon Trotsky. Trotsky advocated Proletarian Revolution as set out in his theory of "Permanent Revolution", as he argued that in countries where the bourgeois democratic revolution had not triumphed already it was necessary that the proletariat carry out the tasks of that revolution and make it permanent by carrying out the tasks of the social revolution at the same time in an uninterrupted process. This theory was advanced in opposition to the position held by the Stalinist faction within the Communist Party that "socialism in one country" could be built in Russia.
Trotsky later developed the position that the Russian workers state had become a "bureaucratically degenerated workers' state". (Eastern European communist governments which came into being without a revolution taking place were later referred to as "deformed workers' states" by the so called Orthodox Trotskyists.) Many of his criticisms were described in his book, The Revolution Betrayed.
Trotskyism has become a by-word used by Stalinists to mean a traitor; in the Spanish Civil War, being called a "Trotskyist" or "Trotskyite" by the Communist supported elements implied that the person was a fascist spy or agent provocateur. George Orwell wrote about this in Homage to Catalonia and in his essay Spilling the Spanish Beans. Note: while both "Trotskyist" and "Trotskyite" are words that were probably originally coined by Stalinists to mark those who sided with Trotsky in factional disputes, "Trotskyist" is a term that is claimed by many, though not all, adherents of Trotsky's views. In fact the term Trotskyist was originally used by the Stalinists to describe that faction of the Communist party, led by Leon Trotsky, that described itself as Bolshevik Leninist, although not used with any great frequency today the term is still used by some. "Trotskyite" retains its pejorative connotation.
In 1938 Trotsky established the Fourth International. After his death this organisation has split many times. Trotskyist parties and groups are notorious for their tendency to split into smaller groups, quarrelling over theoretical differences that seem insignificant or indecipherable to an outsider, but which sometimes have major practical consequences for those who hold those positions.
Many developed countries have several different organizations which claim some tendency of Trotskyism. Among the largest Trotskyist organisations today are the Socialist Workers Party and the Socialist Party (formerly Militant) in Great Britain, Lutte Ouvrière and the Ligue communiste revolutionnaire in France, and the International Socialist Organization in the United States. Two smaller Trotskyist groups are the Spartacist League (see International Spartacist Tendency) and the League for the Fifth International (in Great Britain consisting of Workers Power).