  This is an introductory lecture note aiming at providing an overview of the
AdS-CFT correspondence at weak 't Hooft coupling at finite temperature. The
first aim of this note is to describe the equivalence of three interesting
thermodynamical phenomena in theoretical physics, namely, Hawking-Page
transition to black hole geometry, deconfinement transition in gauge theories,
and vortex condensation on string worldsheets. The Hawking-Page transition and
the deconfinement transition in weakly coupled gauge theories are briefly
reviewed. Emphasis is on the study of 't Hooft-Feynman diagrams in the large
$N$ gauge theories, which are supposed to describe closed string worldsheets
and probe the above equivalence. Nature of the 't Hooft-Feynman diagrams at
finite temperature is analyzed, both in the Euclidean signature (the imaginary
time formalism) and in the Lorentzian signature (the real time formalism). The
second aim of this note is to give an introduction to the real time formalism
applied to AdS-CFT.

High Energy Physics - Theory