I have been contemplating studying some subjects by watching video lectures, more specifically Topology and Quantum Mechanics. I was wondering, if anyone has tried studying a subject on his own by watching just lectures. Alternatively, I could work systematically through a book. What are the advantages and disadvantages of learning by watching lecture videos, compared to reading a book? I am more concerned more about courses in Maths and Physics.
For postgraduate research, neither watching video lectures nor just reading a book are going to help you enough.
You're going to have to actively engage with the subject matter, by solving problems, and keeping up with current research literature in journals.
Following on from the OP's comment: I do understand that your question is "which is better - books or videos". And the answer to your question is neither. It's a false opposition.
Neither are necessary, and neither are sufficient. You have to learn the core content of maths and physics by solving problems. And to do postgraduate research, you have to keep up with the current research literature in journals (including preprint archives where appropriate).
The most important advantage/disadvange IMHO is personal preference.
Looks rather complementary than exclusive to me. Additional self-study (by book) is usually recommended also for (live) lectures. I think it even more important for video lectures, because you cannot ask questions. It will depend on what level of understanding you want to achieve, though.
I have studied through difficult math topics using basically three approaches:
To get the basics of the topic you are studying and "leveling up" with the other people in the field, I think this three resources are very good. I do not see why would you single one out in favor of the other. I've basically seen like 4 Machine Learning Summer Schools, 3 Online Courses, 3 books, and that was only to be aware of what was happening around me.
After that I had to engage a lot on Online communities, conferences, papers, etc.
I find that a good practice is to set alerts for authors that you wish to follow and are prolific in the specific area you are doing your research on.