What does ‘this book’ stand for? And some other questions.

What does ‘this book’ stand for? And some other questions.

The passage below is from The Library: A Fragile History by Andrew Pettegree.

Those who lived in sixteenth-century Oxford and Cambridge probably accumulated

disproportionately large libraries, but this steady upward trajectory is clearly characteristic of English collecting more generally. The undistinguished Mr Mote, who died in 1592, had an extraordinarily fine collection of 500 books, and the London grocer Edward Barlow, his near contemporary, almost 200, most of his books being medical texts to support his apothecary shop. The bibliophilic Thomas Barker, who arrived as a student in Cambridge in the Easter term of 1549, during the short reign of Edward VI, died within two months. Yet he left a library of seventy-five books, including a Greek dictionary, the works of Hippocrates and the Moriae Encomium of Erasmus; he was one of thirty-one Cambridge testators to own this book. His scanty possessions otherwise comprised only his clothing, and a large chest with lock and key, presumably to house his books.

I have some questions on the underlined parts.

Above all, on ‘thirty-one Cambridge testators’.

Do ‘testators’ mean those who leave their will before death? (Am I right?) And does modifier ‘Cambridge’ mean testators are students and faculty of Cambridge university? (Am I right?) And does ‘thirty-one’ mean the number of dead Cambridge people in 1549 alone? (Am I right?)

Lastly, does ‘this book’ refer to ‘the Moriae Encomium’? (Am I right?)

Thanks (for replying SO many trifling questions) in advance.