Mathematical statistics

Classical (aka "frequentist")

Shao, Mathematical statistics

Lehmann and Casella, Theory of point estimation

Lehmann and Romano, Testing statistical hypotheses

Both classical and Bayesian

Schervish, Theory of statistics

Barnett, Comparative statistical inference

Bayesian

Introductory to intermediate

Kadane, Principles of uncertainty

Berger, Statistical decision theory and Bayesian analysis

Bernardo and Smith, Bayesian theory

Advanced

Robert, The Bayesian choice

Hartigan, Bayes theory

Watanabe, Mathematical theory of Bayesian statistics

Information geometry

Amari, Methods of information geometry

Ay et al, Information geometry