What theory was the basis on which the american policy of containment was established?

The theory of George F. Kennan in his "long telegram" provided the basis for containment policy.

George F. Kennan was an American diplomat in Moscow after World War II.  In 1946, he sent what became known as "the long telegram" of his advice about what the USA needed to do about the Union of Soviet Socialist Republics (USSR).  It really was a LONG telegram at 8,000 words.  (Think of how many Twitter messages that would be today!)
In those 1940s, after World War II, everyone feared an ultimate confrontation between the USA and the USSR -- that the Cold War would someday explode into a massive heated conflict between the superpowers.  Kennan, in Moscow, had much foresight to see the internal problems the USSR had.  He advised not pushing the conflict too much, but instead just try to "contain" the Soviet Union and wait for their system to collapse under the weight of its own problems.  Kennan was right.  It took almost 50 years, but eventually the communist system in the USSR fell apart.  [The Union of Soviet Socialist Republics came to an end in 1991.]