Folland, G. B. (2013). Real analysis: modern techniques and their applications. John Wiley & Sons.
Aliprantis, C. D., & Border, K. (2006). Infinite dimensional analysis: a hitchhiker's guide. Springer Science & Business Media.
Durrett, R. (2010). Probability: theory and examples. Cambridge university press.
Munkres, J. (2000). Topology.
Rockefeller, R. (1973). Convex analysis [Russian translation]. Mir, Moscow.
1.2 Math and Econ applications:
Intriligator, M. D. (1971). Mathematical optimization and economic theory(Vol. 39). Siam.
Ok, E. A. (2007). Real analysis with economic applications (Vol. 10). Princeton University Press.
Ok, E. A. Probability with economic applications. In progress.
Ok, E. A. Order theory and its applications. In progress.
Ok, E. A. An introduction to topology. In progress.
2.1 General Textbook:
Mas-Colell, A., Whinston, M. D., & Green, J. R. (1995). Microeconomic theory (Vol. 1). New York: Oxford university press.
Kreps, D. M. (2012). Microeconomic foundations I: choice and competitive markets (Vol. 1). Princeton University Press.
Rubinstein, A. (2012). Lecture notes in microeconomic theory: the economic agent. Princeton University Press.
MWG worth reading for at least three times for every econ student. But for those who are interested in being a theorist, it's not deep enough. More serious treatment is needed and Kreps (2012) would be a great advanced reference. Rubinstein (2012) on the other hand is a well-written but much easier book. Read it for fun and insights.
2.2 Decision and Market:
Fishburn, P. C. (1970). Utility theory for decision making (No. RAC-R-105). Research analysis corp McLean VA.
Chipman, J. S. (1971). Preferences, utility, and demand.
Debreu, G. (1987). Theory of value: An axiomatic analysis of economic equilibrium (Vol. 17). Yale University Press.
Arrow, K. J. (2012). Social choice and individual values (Vol. 12). Yale university press.
Chambers, C. P., & Echenique, F. (2016). Revealed Preference Theory.
Deaton, A., & Muellbauer, J. (1980). Economics and consumer behavior. Cambridge university press.
Arrow, Debreu and Deaton are three super famous and classical books, especially the first two. Fishburn and Chipman are two excellent references for serious technical treatment in decision theory. Chambers & Echenique (2016) is of great help in terms of linking classical topic of choice-based theory to modern applications.
2.3 Game Theory:
Fudenberg, D., & Tirole, J. (1991). Game theory, 1991. Cambridge, Massachusetts, 393.
Myerson, R. B. (2013). Game theory. Harvard university press.
Maschler, M. S., & Zamir, E. Sh.(2013): Game Theory.
Mailath, G. J., & Samuelson, L. (2006). Repeated games and reputations(Vol. 2). Oxford: Oxford university press.
Mertens, J. F., Sorin, S., & Zamir, S. (2015). Repeated games (Vol. 55). Cambridge University Press.
Needless to say, FT is the "Bible" in game theory, just like MWG in microeconomics. Myerson is an extremely insightful one, but you'd better read some other "more standard" game theory textbooks before going to Myerson. MSZ (2013) is more up-to-date, with a nice treatment in epistemic foundation and universal type space part. MS is famous in repeated games, but I haven't read it yet. MSZ (2015) is exciting for its technical style.
2.4 Incentive and Contract:
Laffont, J. J., & Martimort, D. (2009). The theory of incentives: the principal-agent model. Princeton university press.
Salanié, B. (2005). The economics of contracts: a primer. MIT press.
I'm not familiar with this field so sorry for the incompleteness.
2.5 Auction, Matching and Mechanism Design:
Borgers, T., Strausz, R., & Krahmer, D. (2015). An introduction to the theory of mechanism design. Oxford University Press, USA.
Diamantaras, D., Cardamone, E., Campbell, K. A. C., Deacle, S., & Delgado, L. A. (2009). A toolbox for economic design. Macmillan.
Bergemann, D., & Morris, S. (2012). Robust mechanism design. The Role of Private Information and Higher Order Beliefs. Singapore: World Scientific Publishing.
Milgrom, P. R. (2004). Putting auction theory to work. Cambridge University Press.
Krishna, V. (2009). Auction theory. Academic press.
Paarsch, H. J., & Hong, H. (2006). An introduction to the structural econometrics of auction data. MIT Press Books, 1.