Improved bound in Roth's theorem on arithmetic progressions

We prove that if $A\subseteq \{1,\dots ,N\}$ does not contain any non-trivial three-term arithmetic progression, then $$\mathrm{\mid }A\mathrm{\mid }\ll \frac{(\log \log N{)}^{3+o(1)}}{\log N}N\mathrm{.}$$