George Casella and Roger L. Berger, 2002: Statistical Inference, Second Edition, Duxbury.

Ch.1 of Shao (2003) or Keener (2010, Slightly less mathematical than Shao) is recomended in stead of Ch.1 in Casella-Berger (2002) since they use more standard conventions as used in the lectures.

Cramer (1945): Mathematical methods of statistics. (A classic with both philosophy and mathematics in place.)

Sverdrup (1964): Lov og tilfeldighet. Den praktiske statistikks metode og teknikk. Bind 2. En matematisk videreføring. (En nydelig bok inklusive suffisiens og kompletthet med matematikken på plass.)

Cox and Hinkley (1974): Theoretical Statistics (A classic text discussing some of the basic philosophical ideas and problems behind statistical procedures.)

Ferguson (1967): Mathematical Statistics (A classic focused on decision theory)

Keener (2010): Theoretical Statistics. Topics for a Core Course (Similar level as Casella-Berger, but mathematically more precise.)

Shao (2003): Mathematical Statistics. (Similar level as Casella-Berger, but mathematically precise.)

Shao (2005): Mathematical Statistics: Exercises and Solutions (Useful list of Terminology + exercises)

Liese and Miescke (2008): Statistical Decision Theory - Estimation, Testing, and Selection (More general than Berger and using measure theory)

Wainwright (2019): High-Dimensional Statistics. A Non-Asymptotic Viewpoint (A possible second text in Theoretical Statistics. Used in STAT 210B at UC Berkeley.)

Rao (1973): Linear Statistical Inference and its Applications (A very rich text including precise mathematics as needed.)

Berger (1985): Statistical Decision Theory and Bayesian Analysis (A classic.)

Schervish (1995): Theory of Statistics. (Comprehensive mathematical treatment strongly biased towards Bayesian inference.)

Lehmann and Casella (1998): Theory of Point Estimation. (The standard reference.)

Lehmann and Romano (2005): Testing Statistical Hypotheses (Again, the standard reference.)

Stuart et al (2010): Kendall's Advanced Theory of Statistics (3 volumes + more = The 'Bourbaki' of statistics.)

Sir Ronald A. Fisher (1973): Statistical Methods and Scientific Inference (A source for ideas, but not a textbook for an ordinary course.)