\documentclass[
    spinewidth=15mm,
    markcolor=black,
    ]{bookcover}

\usepackage[latin]{babel}
\usepackage{lipsum,microtype}

\begin{document}

% ----------------------------------------------------------------------
% Outside cover
% ----------------------------------------------------------------------

\begin{bookcover}

% Remark
\bookcovercomponent{center}{above front}{
    \textcolor{red}{\textsc{Annales Mathematicae} book cover (outside)}}

% Blue area on the back cover
\bookcovercomponent{tikz}{bg back}{
    \fill[blue!50](7/48,0)--(17.5,24.5)--(17.5,0)--cycle;}

% Blue area on the front cover
\bookcovercomponent{tikz}{bg front}{
    \fill[blue!50](0,0)--(0,24.5)--(833/48,0)--cycle;}

% Background color on the spine
\bookcovercomponent{color}{bg spine}{blue!50}

% Title on the spine
\bookcovercomponent{center}{spine}{
    \rotatebox[origin=c]{-90}{\large\bfseries
        ANNALES MATHEMATICAE 43.~(2020)}}

% Text and picture on the front cover
\bookcovercomponent{normal}{front}[22mm,20mm,22mm,40mm]{
    \centering
    {\huge\bfseries ANNALES\\ MATHEMATICAE\\[13mm]}
    {\large\bfseries TOMUS 43.~(2020)}
    \vfill
    \includegraphics{./figures/bookcover-pi.pdf}
    \vfill
    {\large COMMISSIO REDACTORIUM}\\[3mm]
    \lipsum[2]}

% Text on the back cover
\bookcovercomponent{normal}{back}[22mm,10mm,22mm,30mm]{
    {\centering\large ABSTRACTUM\\[5mm]}
    \lipsum[1-4]}

\end{bookcover}

% ----------------------------------------------------------------------
% Inside cover
% ----------------------------------------------------------------------

\begin{bookcover}

% Remark
\bookcovercomponent{center}{above inside back}{
    \textcolor{red}{\textsc{Annales Mathematicae} book cover (inside)}}

% Background color on the whole inside cover
\bookcovercomponent{color}{bg whole}{blue!50}

% Text on the inside back cover
\bookcovercomponent{normal}{inside back}[22mm,10mm,22mm,30mm]{
    \color{white}
    {\centering\bfseries
    ANNALES MATHEMATICAE\\[3mm]
    Acta internationalis mathematicae\par}
    \bigskip
    \lipsum[1]}

\end{bookcover}

\end{document}