Here we will be taking the quickest of looks at Constructivism and Connectivism learning theories. Constructivism, the more well-known learning theory, was brought to light by several researchers based in the idea that learning is both active and built upon experiences of the learner to construct knowledge. Here is a website with the highlights.
George Siemens was one of the leading researchers on Connectivism. Siemens published this article in the International Journal of Instructional Technology and Digital Learning did back in 2005 that gives a much better overview than say, Wikipedia. Siemens was also interviewed and recorded on the same subject in 2014. This should give you at least the flavor of his perspective.
One of the other researchers on Connectivism was Stephen Downes. He published an ebook in 2012 called Connectivism and Connective Knowledge.