Introductory

Ralph P. Boas, A Primer of Real Functions, MAA, 1972.

Edward Gaughan, Introduction to Analysis, Brooks/Cole, 1968.

Serge Lang, Undergraduate Analysis, Springer-Verlag, 1968.

Walter Rudin, Principles of Mathematical Analysis, McGraw-Hill, 1964.

Georgi A. Shilov, Elementary Real and Complex Analysis, MIT, 1973.

Advanced

Sterling K. Berberian, Measure and Integration, Chelsea, 1970.

Edwin Hewitt and Karl Stromberg, Real and Abstract Analysis, Springer-Verlag, 1969.

H. L. Royden, Real Analysis, MacMillan, 1968.

Walter Rudin, Real & Complex Analysis, McGraw-Hill, 1987.

Ernst Lindelöf, Differentiali- ja integralilasku ja sen sovellutukset I - IV (Differential and integral calculus and its applications), WSOY and Mercatorin Kirjapaino, Helsinki, 1928-1946.

G. E. Shilov and B. L. Gurevich, Integral, Measure and Derivative: A Unified Approach, Prentice-Hall, 1966.

Additional Topic

non-Newtonian calculus