The members of the Leopoldina are organized in 28 sections that are grouped in four classes.
In 1878 the Leopoldina moves with its President, Carl Hermann Knoblauch (XV. President, 1878-1895), to the Prussian university town of Halle (Saale). The Academy concentrates on producing valuable publications and makes its extraordinary collection of books accessible.
In 1879 the Academy library moves from Dresden to Halle and in 1904 an exceptionally modern and practical library building is erected.
The Leopoldina enjoys an excellent reputation during the presidency of mathematician Albert Wangerin (XVII. President, 1906-1921) and is invited to participate in important international events including the Linné celebrations in Uppsala and Stockholm in 1907 and the Darwin celebrations in Cambridge in 1909.
In 1921 another mathematician, August Gutzmer from Halle, becomes President (XVIII. President, 1921-1924). He leads the Academy through the difficult period of hyperinflation in Germany.