Pope Benedict XVI is not the first Pontiff to have published a book whilst Pontiff.
In 1923, Pope Pius XI (Achille Ratti) published Climbs on Alpine Peaks. As a young man, he had been an expert mountaineer and alpinist. The book records his ascent of Monte Rosa (Dufour Peak), the first traverse of the Zumsteinjoch, the ascent of the Matterhorn and the ascent of Mont Blanc and descent by the Dome Glacier.
In fact, in 1890, he was part of the original team which discovered the normal Italian route (West Face direct) on their descent of Mont Blanc. Today the route is known as the "Via Ratti - Grasselli".
He made his last climb in 1913.
However he was always and remained a member of the Club Alpino Italiano and often contributed articles for Club publications.
In Britain, there is a mountaineering club called The Achille Ratti Climbing Club