These are some fundamental books on methodology of scientific research (I missed popper though which is sort of important). I did this course in college and this is primary literature in syllabus. We have read individual parts from each of this books and we did one complete reading of our choice. You have to know some basics of logic and mathematics to fully understand material.
Kolmogorov and Edwint T. Jaynes - probability, statistics (edwin is secondary since theres things like bayes theorem that kolgomorov dosent cover)
Nelson Goodman, David Hume - induction and problems of induction, philosophy of science
Karl Popper (not posted) - demarcation
Thomas Kuhn (not posted) - sort of criticism of popper
I recommend that you look at specific chapters and find things that interest you - since reading everything might be overwhelming.