Sightseeing
Leipzig Zoo (Pfaffendorfer Str. 29, www.zoo-leipzig.de/ ) -- one of the best German zoos.
Monument to the Battle of Nations (Str. des 18. Oktober 100, Stiftung Völkerschlachtdenkmal Leipzig (stiftung-voelkerschlachtdenkmal-leipzig.de) ) -- large monument for the largest battle of Napoleonic wars
Thomaskirche (Thomaskirchhof 18, Thomaskirche Leipzig | Startseite ) -- Bach worked there for 27 years.
City Center -- it is a nice walk and contains several interesting museums
Leipzig Mathematics:
Leipzig has a long mathematical tradition. One of its earliest renowned figures was August Ferdinand Möbius (1790–1868), who studied and spent essentially his entire academic career at Leipzig University. Leipzig became an especially prominent center of mathematics in the 1880s. Felix Klein (1849–1925) held the chair of geometry there from 1880 to 1886 and established the Mathematical Seminar, attracting a remarkable circle of young mathematicians. His Leipzig period included important work on geometry, function theory, and the theory of the icosahedron. When Klein moved to Göttingen, he was succeeded in 1886 by Sophus Lie (1842–1899). During Lie's twelve years in Leipzig, the theory of continuous transformation groups—what we now call Lie groups and Lie algebras—was developed and systematized. Further mathematicians who worked in Leipzig for a long time include Otto Hölder, Felix Hausdorff, Paul Koebe, Leon Lichtenstein, Karl Rohn, and Bartel van der Waerden.