  In his 1947 paper that inaugurated the probabilistic method, Erd\H{o}s proved
the existence of $2\log{n}$-Ramsey graphs on $n$ vertices. Matching Erd\H{o}s'
result with a constructive proof is a central problem in combinatorics, that
has gained a significant attention in the literature. The state of the art
result was obtained in the celebrated paper by Barak, Rao, Shaltiel and
Wigderson [Ann. Math'12], who constructed a
$2^{2^{(\log\log{n})^{1-\alpha}}}$-Ramsey graph, for some small universal
constant $\alpha > 0$.
  In this work, we significantly improve the result of Barak~\etal and
construct $2^{(\log\log{n})^c}$-Ramsey graphs, for some universal constant $c$.
In the language of theoretical computer science, our work resolves the problem
of explicitly constructing two-source dispersers for polylogarithmic entropy.
