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I would like to have all of my page numbers on the top right of my pages and for now it does so only for my pages without a ,\part or \chapter.

Furthermore, I would like my pages before my in introduction (table of content and table of figures) to have roman numbers on the top right (for now there are arabic numbers in the bottom middle).

Here is my code:

\documentclass[a4paper,twoside,12pt]{report}

\usepackage[top=2.5cm, bottom=2.5cm, left=2.5cm, left=2.5cm]{geometry}
\setlength{\parskip}{0.2cm}

% A lot of packages here I won't include to make it as clear as possible
\usepackage{fancyhdr}
\pagestyle{plain}
\titleformat{\chapter}[display]
   {\normalfont\huge\bfseries}{\chaptertitlename\ \thechapter}{20pt}{\Huge}
\titlespacing*{\chapter}{0pt}{0pt}{10pt}


\begin{document}

\begin{titlepage}
  \includepdf{cover}
\end{titlepage}

\tableofcontents

\thispagestyle{empty}

\clearpage
\listoffigures

\cleardoublepage %The first chapter should start on an odd page.

\pagestyle{fancy}
\fancyhf{}
\fancyhead[R]{\thepage}

\setcounter{page}{1}

\chapter{Introduction}

lot of text

\part{part 1}

\chapter{chapter 2}

lot of text

\section{section 1}

\subsection{subsection 1}

etc.


\cleardoublepage

\includepdf{back}

\end{document}

Thank you very much

1

Maybe the following helps:

\documentclass[a4paper,twoside,12pt]{report}
\usepackage[top=2.5cm, bottom=2.5cm, left=2.5cm, left=2.5cm,
  headheight=14.5pt% as suggested by fancyhdr
]{geometry}
\usepackage[skip=.2cm,indent]{parskip}% do not change \parskip manually

\usepackage{fancyhdr}
\pagestyle{fancy}
\fancyhf{}
\fancyhead[R]{\thepage}
\renewcommand\headrulewidth{0pt}
\fancypagestyle{plain}{
  \fancyhf{}
  \fancyhead[R]{\thepage}
  \renewcommand\headrulewidth{0pt}
  \renewcommand\footrulewidth{0pt}
}

\usepackage{titlesec}
\titleformat{\chapter}[display]
   {\normalfont\huge\bfseries}{\chaptertitlename\ \thechapter}{20pt}{\Huge}
\titlespacing*{\chapter}{0pt}{0pt}{10pt}

\usepackage{blindtext}% only for dummy text in a MWE
\begin{document}
\begin{titlepage}
  \centering\Huge Cover
\end{titlepage}
\thispagestyle{empty}

\cleardoublepage
\pagenumbering{roman}

\tableofcontents
\listoffigures

\cleardoublepage
\pagenumbering{arabic}

\chapter{Introduction}
\Blindtext[2]
\part{part 1}
\chapter{chapter 2}
\blindtext
\section{section 1}
\subsection{subsection 1}
\blinddocument
\end{document}

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