A very obvious thing to do would be to figure out what the university curriculum is, find reference book covering that, and start studying it daily. But, is there anything specific that people here could advice me to do?
I ask because, from what I understand, the fail rates are insane in Germany, and therefore I would to have some advice for success.
Back when I studied math in the later Pleistocene (so, starting in 1996), the key reason for people quitting was that they had wrong expectations: they expected German university math to be like Gymnasium math, maybe a little harder. Many of them had never seen a proof. Then our professor spent the first ten minutes on field axioms. This was a major culture shock.
Quite a number of people left after the first lecture and never came back. I think this may have been a smart move.
Other people stuck it out for a few semesters and left later. Often, these were Lehramtsstudenten, i.e., people studying to become Gymnasium teachers, many of whom took one subject they liked (e.g., sports) and one subject that would get them a job (e.g., math). Yes, many of those were successful. But many lost a number of semesters before they called it quits on math.
Therefore, my suggestion would first of all be to understand what you are getting into. Find almost any book called "Analysis I" or similar and start reading from the beginning. You will not understand a single word at first. Re-read the first section a couple of times. You will see, after a while, that things actually make a kind of sense. There are typically no prerequisites. Everything is right there. The key stumbling block is that studying math requires a way of thinking you never have been exposed to in school. (Except possibly if you did math competitions.)
This is the kind of thing you will be doing for three years, or more. Imagine yourself doing this, over and over again. You will be sitting in class, keeping track of someone explaining this to you. Again, you will typically not understand much during the lecture. So you go home (or, better, meet with others in the same boat), go over everything and try to understand. Then you will do homework, each single piece of which is like a math competition, and you get at least two of these each and every week.
I usually describe studying math as brainwashing. Math professors don't like this description. But I believe it captures the important idea.
Now, after you have slogged through the first chapter of your "Analysis I" book, think about whether the prospect of doing this for years on end resonates with you. If yes, and if you maybe even find this fascinating, congratulations, you are now better prepared than probably 50% or 80% of incoming math students.
If you now still want to study math, then I would suggest you go get a few books on how to write proofs, and how to think mathematically. If you can already access your university library, there will likely be a lot there. You may even be able to download ebooks. Springer has a number of series of undergraduate math textbooks (e.g., Springer Studium Mathematik - Bachelor or Grundstudium Mathematik or the Springer Undergraduate Mathematics Series or the Undergraduate Texts in Mathematics), some of which are in exactly this vein. For instance, judging from the titles, you could look at Mathematisches Problemlösen und Beweisen or Exploring Mathematics by the same author, or perhaps Mathematical Writing.
In addition, sometimes universities offer refresher courses in math before the first semester starts. These can be helpful, too. Just be careful: if these are refresher courses for Gymnasium math which are mainly aimed at students in other disciplines that may use math in "the Gymnasium way", then this will likely not be very helpful to you.
Finally, the Fachschaft (which is kind of the students' self-organization) can be helpful. They all were first semester students once and likely still remember, and can offer lots of hints. (But note that there is a selection effect: these are the ones that are still around. The ones that quit math are elsewhere.) They might organize information sessions at the start of the semester.
And actually, from my understanding this applies to most European math programs. I believe that matters are quite a bit different in the US, with far less emphasis on "proof mathematics" in early semesters.
If it is your first semester ( I assume that ), and if you will move to Germany for the very first time, you would like to get all bureaucratic acts and hassles done before the semester starts. Things are tough these days in Germany, with staff shortages and long processing times. Likewise, try to secure an apartment / a dormitory room a while before the semester starts. Familiarize yourself with your new surroundings so that you can focus on studying once the semester has started. The better you speak the language, the better for you.
There won't be a reference book covering the entire curriculum but individual books and/or other course material covering individual courses.
Follow the directions of the professors. Take a lot of notes. Practice summarizing your notes. Do a lot of exercises, even beyond the ones assigned. Look for insight beyond the details. Ask as many questions as you can. Listen to the answers. If permitted, form a study group to discuss things and aid in gaining insight. Follow the rules set. Take advantage of professors' office hours.
Don't expect that lectures are enough to teach you. Don't depend too much on technology.
Try to get feedback on the exercises you do. This might be automatic, or you might need to see it out.
Get enough sleep, especially before exams. Get enough exercise. Eat properly. Use good judgement about things in life. Do more exercises.
Not limited to Germany, nor to math. Not even limited to a bachelors.
Pay attention really well when they introduce you to LaTeX. In my batch (started 2019), proficiency in LaTeX correlates positively with your grades. After all, you can't use MathSE properly without knowing LaTeX.
Jokes aside, MathSE is your friend. Trying to write a coherent question often clears up confusions. Forming actual sentences from a chain of intuitive thoughts is not easy, and requires systematic thought. Once you start thinking systematically, often the confusion is immediately identified, you missed an assumption, misunderstood an axiom, etc.
Also, do not worry too much if you feel like you don't understand things in the first year. Eventually, you will develop enough mathematical maturity to be comfortable with the Definition-Theorem-Proof system. Once you understand how this system works, you can then revisit your early calculus/analysis/linear-algebra classes to truly understand it, and things are beatiful after this point. Myself, I only truly understood single-variable calculus in my third year, after passing a differential geometry course (don't ask me how)!
