What prerequisite courses do I need in order to specialize in Mechanism/Market design theory? After seeing some lectures on Youtube, I came to learn about a few, namely, Game Theory and Microeconomics, but I am not sure whether this is all that is needed. Please do add as many courses as possible or refer to the courses that should be taken from the following list: http://www.lse.ac.uk/resources/calendar/programmeRegulations/undergraduate/BScEconomics.htm
The list you posted was for an undergraduate degree in economics. Mechaism design usually won't come up in any serious way until graduate school. Until then, my advice is to take as much as the following as possible: 


microeconomic theory, 
game theory (often covered within microeconomic theory), 
mathematical methods/optimisation.


Mechanism design falls under the rubric of microeconomics theory, which at the advanced (i.e. postgraduate) level is highly technical. So achieving a high degree of mathematical sophistication in addition to a solid grounding in microeconomic theory is probably the best strategy.