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Re:Kolmogorov Complexity (2014) [pdf] by sewercake on Wednesday May 18, 2016 @11:13AM (#11722522)
http://inference-review.com/article/doing-mathematics-differ...

While I don't have a text book for you, I found this article by Gregory Chaitin (a notable academic in the same sphere as kolmogorov et al) to be very exciting / enlightening.

Re:Kolmogorov Complexity (2014) [pdf] by rfreytag on Wednesday May 18, 2016 @11:41AM (#11722722)
Kolmogorov-Chaitin Complexity is another term for the same concept (as per the OP Wikipedia article).