There are 2 train companies operating 8 routes - EC62, CNL 1258, IC60, IC62, ICE42, IC26, 701, RJ63. The cheapest train costs $70 and is 3h 2min.
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There are 3 ways to travel from Augsburg to Heidelberg. 1 bus, 3 trains and 1 by car are possible between the two areas. The by car from Augsburg to Heidelberg is the cheapest. The train operated by DB running from Neusäß to Heidelberg is the fastest. The train operated by DB running from Augsburg Hbf to Heidelberg is the most convenient.
It's important to check each mode when booking your ticket so that you can find the best method for you. The cost of each type varies differently, so be sure to use Faretrotter to keep an eye out!