In addition to the lectures, you will of course work with one or the other book. Most lecturers will give you recommendations for literature or base their lectures on a specific book. It also doesn't hurt to take a look around for yourself. The only important thing is that you don't rush to buy books yourself, but look at them calmly and borrow them first. You have to be able to really work with the book, otherwise you won't get anything out of it.
Warm recommendation: Instead of getting angry that a certain book that you urgently need for your exam preparation is out of stock in the library, just use the opportunity of the purchase suggestion! Here you simply enter the title of the book and a little more information, and maybe the book of your choice will be available for you to borrow after a week.
Many books from Springer-Verlag are available online as pdf. You can either go directly to http://www.springerlink.com or find the book as an "electronic resource" in the library search. Access to the e-book is only possible in the HU network (i.e. on site or VPN). Since the search on the Springerlink page is very cumbersome, the library page is recommended.
You are also welcome to drop by the student council room, where we have put together a small library for you, in which you can find some of the standard textbooks.