Mantua IT is a city and comune in Lombardy. See here for more information: https://en.wikipedia.org/wiki/Mantua
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University professor of mathematics and academic in Vienna
1850 Major and commander in Maestre [referring to Mestre in Italy, especially since his wife is from Como, so he most likely spent time in Italy. See https://en.wikipedia.org/wiki/Mestre for more information] and then retired in Vienna
Corporal for the Princes of Schwarzenberg in Lobesitz [Corporal was the lowest non-commissioned officer rank in German infantry forces designated as Jäger]