My own field, ergodic theory, is relatively young in that some concepts now regarded as fundamental -- Kolmogorov-Sinai entropy, for example -- were not formulated until around 1960. Nonetheless there are a couple of old books still in use and receiving citations:

E. Hopf, Ergodentheorie, 1937;

R. Halmos, Ergodic theory, 1957.

If the 1960s are sufficiently long ago to constitute "old" then there are many old references in probability which remain in heavy use, for example:

P. Billingsley, Convergence of probability measures, 1968;

L. Breiman, Probability, 1968;

and one of the classics of the field:

W. Feller, Introduction to probability theory and its applications, 1950.

Outside my own field, a much-cited number theory text which no-one has yet mentioned:

A. Khinchin, Continued fractions, 1936.

My own field, ergodic theory, is relatively young in that some concepts now regarded as fundamental -- Kolmogorov-Sinai entropy, for example -- were not fully formulated until around 1960. Nonetheless there are a couple of old books still in use and receiving citations:

E. Hopf, Ergodentheorie, 1937;

R. Halmos, Ergodic theory, 1957.

If the 1960s are sufficiently long ago to constitute "old" then there are many old references in probability which remain in heavy use, for example:

P. Billingsley, Convergence of probability measures, 1968;

L. Breiman, Probability, 1968;

and one of the classics of the field:

W. Feller, Introduction to probability theory and its applications, 1950.

Outside my own field, a much-cited number theory text which no-one has yet mentioned:

A. Khinchin, Continued fractions, 1936.