Discussion: Mathematically precise physical textbooks I am very interested in the abstract mathematical description of nature. Therefore, I have recently started to compile a list of good textbooks about physics, which have a very high level of mathematical rigour. Of course, I am aware that the physical unterstanding of theories and also the use of some "hand-wavy" mathematics as abbreviation is indispensable, but as I have seen by similar questions in this and other forums, I am not the only one who enjoys reading abstract mathematical textbooks about physics. 
By the way, I do not mean books about mathematical methods of physics. I am not a really big fan of such textbooks, because I think that one should read a real matehmatical textbook in order to learn the underlying mathematics of physics. But of course, there are some very good books about this topic, like the german textbook series "Mathematische Methoden der Theoretischen Physik" from the Austrian physicist Gebhard Grübl or also Hassani's book "Mathematical physics".
With this thread, I would like to hear some opinions and also some additional suggestions for my list:
(1) Classical physics (mechanics + electrodynamics):


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*Arnold: "Mathematical Methods of Classical mechanics" - a clasic one but still good

*Lee, Leok and McClamroch: "Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds: A Geometrical Approach to Modeling and Analysis" - A nice book about Lagrangian mechanics on manifolds

*Gross, Kotiuga, Knovel and Levy: "Electromagnetic Theory and Computation: A Topological Approach" - I do not have a very deep look into this book but it seems to be mathematical precise.
(2) Special and general theory of relativity:


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*Gourgoulhon: "Special relativity in General Frames: From Particles to Astrophysics"

*Naber: "The Geometry of Minkowski Spacetime: An Introduction to the Mathematics of the Special Theory of Relativity"

*O'Neill: "Semi-Riemannian Geometry With Applications to Relativity"

*Godinho and Natario: "An Introduction to Riemannian Geometry: With Applications to Mechanics and Relativity"

*Köhler: "Differentialgeometrie und homogene Räume" - This book is in german language and more about differential geometry. However, the last two chapters include a very precise and axiomatic description of the foundation of general relativity and also a little bit of Kaluza-Klein theory.....
(3) Quantum mechanics:


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*Teschl: "Mathematical Methods in Quantum Mechanics: With Applications to Schrödinger Operators"

*Takhtadzhian: "Quantum Mechanics for Mathematicians"

*Gustafson: "Mathematical Concepts of Quantum Mechanics"
(4) Quantum feld theory and gauge theory:


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*Zeidler: "Quantum Field Theory - A Bridge between Mathematicians and Physicists" volume I, II and III - Although these books are a little bit chaotic, I think they include some very nice approaches. Unfortunately, the author was only able to finish 3 out of 6 books of the planned series.

*Deligne et. al.: "Quantum Fields and Strings: A Course for Mathematicians" - What would be a list about mathematical physics books without Edward Witten...

*Hamilton: "Mathematical Gauge Theory: With Applications to the Standard Model of Particle Physic" - a very good textbook about gauge theory 

*Baum: "Eichfeldtheorie: Eine Einführung in die Differentialgeometrie auf Faserbündeln" - in german language
Of course, also books of other disciplines of physics are welcome. 
EDIT: For some reason, my question was closed because it is not "focused" enough.....Therefore, I have (unfortunately) to restrict my question a little bit and asking therefore to focus on books about topics similar to that one mentioned above in my list: Quantum and classical mechanics, relativity and (classical and quantum) field theories.....But still, recommandations of other topics are welcome as comments.....
 A: Here's a partial list for classical equilibrium statistical physics. I restricted it to books covering a "large" area; there are of course many other books focusing on very specialized topics. I also only listed mathematically rigorous works. 
Note: I have not cited books on integrable systems. First, because I am not a specialist. Second, because some of those I know are not mathematically rigorous (even if they are very good and useful books). Somebody else can list them if they think they should be present.
General textbooks


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*Statistical Mechanics: Rigorous Results, D. Ruelle

*The Statistical Mechanics of Lattice Gases, B. Simon

*Statistical Mechanics of Lattice Systems: a Concrete Mathematical Introduction, S. Friedli and Y. Velenik

*Stochastic Processes on a Lattice and Gibbs Measures, B. Prum

*Scaling Limits in Statistical Mechanics and Microstructures in Continuum Mechanics, E. Presutti

*Introduction to Mathematical Statistical Physics, R. A. Minlos

*Theory of Phase Transitions: Rigorous Results, Ya. G. Sinai


Large deviations


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*Entropy, Large Deviations, and Statistical Mechanics, R. Ellis


Disordered systems


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*Statistical Mechanics of Disordered Systems: A Mathematical Perspective, A. Bovier

*Mean Field Models for Spin Glasses: Volume I, Basic Examples, M. Talagrand

*Mean Field Models for Spin Glasses: Volume II, Advanced Replica-Symmetry and Low Temperature, M. Talagrand


(To be honest, the two last books above deal with a rather specific problem, but given their importance, I felt I had to list them.)
Books more aimed at mathematicians


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*Gibbs Measures and Phase Transitions, H.-O. Georgii

*Convexity in the Theory of Lattice Gases, R. B. Israel

*Gibbs Random Fields: Cluster Expansions, V.A. Malyshev and R. A. Minlos

*Thermodynamic Formalism: The Mathematical Structures of Classical Equilibrium Statistical Mechanics, D. Ruelle

A: Landau & Livshits series is 10 volumes of theoretical physics written on a high mathematical level, although some newer subjects may not be present there. (Note that not all of them have Landau and/or Livshits as the actual authors). In general, Soviet-era Russian textbooks  tend to be more mathematical then their western counterparts... they obviously do not contain the developments of the last three decades, but the essential physics is still valid.
Note also that when Russians talk about theoretical physics or generally add adjective theoretical they mean specifically mathematical theory of physical phenomena, as opposed to applied physics or domain-specific names (nuclear physics, hydrodynamics, etc.) which focus more on the physical phenomena (even if written at high mathematical level). 
