\documentclass{amsart}
\usepackage[svgnames]{xcolor}
\usepackage[hmargin=16mm]{geometry}
\usepackage{graphicx}
\usepackage{lipsum}
\usepackage{hyperref}

% number figures within sections
\counterwithin{figure}{section}

% a hack to fix a bug when using caption with amsart...
\makeatletter\def\@dotsep{4.5}\makeatother

% figure and subfigure specifications
\usepackage{caption}
\usepackage[list=true,listformat=simple]{subcaption}

\author{A ghost writer}
\title{Some nicer figures}

% change only after this line
\hypersetup{%
  pdftitle={Some nicer figures},
  pdfauthor={A Ghost writer},
  colorlinks = true,
  linkcolor = DarkBlue,
  anchorcolor = red,
  citecolor = blue,
  urlcolor = BlueViolet
}

\begin{document}

  \begin{abstract}
    For this exercise you need to work out how to add the author and title 
    as metadata for the PDF file, add an external link 
    to the ctan page for \textcolor{DarkViolet}{hyperref}, 
    type set \textcolor{DarkBlue}{Figure 1.1} and \autoref{Figure 2.1}
    together with the subfigures \textcolor{DarkBlue}{Figure 1.1a}, 
    \textcolor{DarkBlue}{Figure 1.1b} and \textcolor{DarkBlue}{Figure 1.1c}. 
    On top of that, you will need to find 
    some interesting colours. 
  \end{abstract}


\maketitle 

\tableofcontents

\listoffigures

\part{A subfigure example}

{A figure example}


\begin{figure}[htbp]
\centering
\begin{subfigure}{30mm}
\includegraphics[width=30mm]{example-image-a}\label{fig.1a}
\caption{caption a}
\end{subfigure}
\begin{subfigure}{30mm}
\includegraphics[width=30mm]{example-image-b}\label{fig.1b}
\caption{caption b}
\end{subfigure}
\begin{subfigure}{30mm}
\includegraphics[width=30mm]{example-image-c}\label{fig.1c}
\caption{caption c}
 \end{subfigure}
 \section{A subfigure example}
\lipsum[1]\label{fig.1}
\caption{a nice picture}
\end{figure}

  \lipsum[2-3]
  
\begin{figure}
  \section{A figure example}
  \lipsum[4]\label{fig.2}

    \includegraphics[width=55mm]{example-grid-100x100bp}
    \caption{random grid}
  \lipsum[5]
\end{figure}

\end{document}