Your doctoral thesis is the first contribution to your field of research, and lays the foundations for your subsequent career in academia. That's why it's so important to choose the right topic. It should be more than simply a topic that's relevant to the academic field — it should concern something you feel passionate about!
Following completion of a State Examination (Staatsexamen), Diplom (German academic degree), Magister (German academic degree) or master's degree, candidates can apply for a doctoral degree. Promotionsordnung (doctoral degree regulations) for each subject determine who is eligible. In most cases, above-average academic performance in the preceding degree program is a prerequisite for acceptance to becoming a doctoral candidate.
The core component in doctoral studies is the independent preparation of an extensive academic research paper (dissertation), which must be published. In addition, some subjects require successful candidates to fulfill further requirements. Doctoral studies conclude with a comprehensive final examination ("Rigorosum") or a so-called Disputation, in which each doctoral candidate presents their doctoral thesis to the public and engages in a specialist discussion with university lecturers.
If you're thinking about your dissertation, you're probably working on your master's degree right now. As a first step, consider the field you're interested in and, based on that, define your desired research direction. Read the most recent literature and identify an issue that you feel has not been adequately addressed within the academic world.
As a second step, you should identify eligible doctoral supervisors, whose research profile and interests fit your project idea. An alternative approach is to contact the appropriate institute in your faculty.
It can also be useful to look at advertisements for doctoral positions or for structured doctoral programs.
In the natural and life sciences, specific doctoral topics are often advertised, especially if the position is part of an externally funded project. You can find these either directly on each institution's website or on the LMU job portal.
Once you have decided on a potential supervisor, you can contact them directly. If you have reached an agreement with your future supervisor or have been accepted into a structured doctoral program, you are ready to let yourself be accepted as a doctoral candidate in the faculty concerned.