why is the Cognitive theory the most popular among contemporary therapists.
I'm not sure what you mean by "popular." Very often therapists are relatively eclectic, using the best aspects of several theories rather than just one. It also depends on which cognitive theory you are discussing.
http://www.personalityresearch.org/cogsocial.html
http://allpsych.com/personalitysynopsis/cognitive.html
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http://www.personalityresearch.org/papers/allen.html
http://en.wikipedia.org/wiki/Cognitivism_(psychology)
http://www.findarticles.com/p/articles/mi_g2699/is_0004/ai_2699000416
http://en.wikipedia.org/wiki/Albert_Ellis
I hope this helps. Thanks for asking.