I hear that many universities (at least in my country) award best thesis award every in every department. I want to review such thesis in mathematics to get updated with current levels of research going on in different field of mathematics. Is there a way I can get access to it.
I suspect that learning about "current levels of research" in mathematics won't be well represented if you only look at the award winners. I think you will need a much broader sort of search to get an idea about what is really going on and what is generally accepted in current doctoral research.
And not all "current levels of research" is even represented in doctoral theses in the first place. Among the awards, you are more likely to see only theses in relatively "hot" areas of research, and miss the overall picture.
Note that research in really hard areas of mathematics isn't the best candidate for a dissertation problem as the probability of success in a limited time frame is much lower.
If you are asking the question because you are looking to choose your own topic, then you should also note that research in a "hot" area is a bit risky as others are also working there feverishly, and you have a higher probability of getting scooped.