When you arrive in Mannheim, you will have 5 options for getting around other than your feet. The taxi (which is expensive for long term use), a bike-share (which you will have to sign up for from Nextbike, so you probably won’t have this option until you get access to the internet), and of course the train, tram, and bus.
After you get your matriculation number from the international office (when you register with them), it is best if you get your semester pass, which will allow you to use the trains which travel out to about 50km (about 31 miles…get used to hearing things in the metric system, they don’t use the standard system here) from Mannheim, trams and buses. But, the RNV/VRN will only allow the use of the semester ticket from the times dated on your paperwork saying you are a student at Mannheim. Assuming you arrive a few days prior to the beginning of the semester, or are taking the summer or winter academy, which begins about a month prior to the regular semester, how do you get around since the semester pass is still not valid?
Purchasing an individual ticket cost 2.50 euro PER VEHICLE you board. That gets expensive fast as well. But you can also purchase a day pass for 6.5 euros, which is only good from 12:00am until 11:59pm. Keep the time in mind when purchasing the daily pass. If you know you are going to go home after midnight, your ticket won’t be valid, and you will have to pay again. But if you are traveling around for the day and will need more than 3 different rides, it will be worth it. Simple math gives you a ride to, and then back from 1 location, it would be best to get individual tickets for the rides (since you boarded only 2 different vehicles). However, if you will need to get on more than 3 vehicles to get to your location (and then back), get the day pass if you can get it all done before 11:59pm. This ticket allows you to get around by tram and bus, but not the train (you will need to purchase tickets at the train station for those rides).
The other option that NO ONE at the RNV/VRN will share or hint at is to purchase a weekly pass. Apparently, you can only get this pass on Monday. It cost 19 euros for the week, and will enables you to get around by train, tram and bus for the week (again, Monday from time of purchase until Sunday at 11:59pm). This makes exploring for the week much more affordable, assuming you were to purchase a daily pass for the 7 days (45.50 euros compared to 19 euros). Additionally, this pass will give you more range in that you can also use it on trains, although only on regional trains which generally go up to 50Km, and not the Inter-City (IC) or Inter-City Express (ICE) trains.
You can of course try (I highly recommend you NOT do this thou) just jumping on the trains and buses during the day, and hope you don’t get asked to present your ticket. The Germans do however, have people who’s job it is (on the trains mostly) to check to see if you have a ticket. If you get caught riding around without a ticket on the trains, trams or buses, it’s a 60 euro fine for the 1st offense. Apparently the subsequent fines after are more expensive, and the police also get involved. Bus drivers tend not to check your pass during the day, but at night they won’t let you on without checking, so you would have to pay upon boarding anyway. Trams rarely have ticket checkers, but it does happen. Trains almost always have those employees checking for “free riders” and they will eventually catch you. I’ve witnessed a number of people getting caught, and besides the embarrassment of everyone around you (well, those who speak German) knowing you weren’t following the rules and got caught, there is the 60 euro fine as well which is much more expensive than having bought a ticket would have been.