documentclass[12pt,twoside]{book}

usepackage{fancyhdr}
fancyhead{} % clear all header fields
fancyhead[LO]{nouppercaseleftmark}
fancyhead[RE]{nouppercaserightmark}
fancypagestyle{plain}{%
fancyhead[LO]{nouppercaseleftmark}
fancyhead[RE]{nouppercaserightmark}
}
%renewcommand{headrulewidth}{0pt} % no line in header area
fancyfoot{} % clear all footer fields
fancyfoot[LE,RO]{thepage}           % page number in "outer" position of footer line
fancyfoot[RE,LO]{today} % other info in "inner" position of footer line
fancypagestyle{plain}{%
fancyfoot[LE,RO]{thepage}           % page number in "outer" position of footer line
fancyfoot[RE,LO]{today} % other info in "inner" position of footer line
}
begin{document}

chapter*{Contents}

chapter{Introduction}

This is the first section.

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neque pharetra sollicitudin.  Praesent imperdietmi nec ante.
Donec ullamcorper, felis non sodales...

end{document}