The public transportation in Leipzig consists of trains, trams and buses. The operating company of tram and bus lines is called Leipziger Verkehrsbetriebe (Leipzig Transport Company):
https://www.l.de/verkehrsbetriebe/fahrplan

If you want to explore Leipzig's surroundings beyond the Leipzig Transport Services or want to visit other parts of Germany or its neighbors to the East and South, Austria, Poland and the Czech Republic, you can travel by train with Deutsche Bahn (German Railway):
https://www.bahn.com/en/view/index.shtml