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I would like to know if there are compendiums much like the Princeton Companion to Mathematics for physics (especially classical physics: fluid mechanics, elasticity theory, Hamiltonian formalism of classical mechanics, statistical mechanics etc etc).

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I voted to close as off-topic in order for this question to be migrated to Physics –  t.b. Oct 19 '11 at 0:10
    
Landau & Lifshitz? –  Robin Ekman Feb 14 at 16:21

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In this question the Companion was suggested as a math equivalent of the Feynman Lectures on Physics. If this is an equivalence relation it should be symmetric.

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Feynman lectures on Physics is outdated and not really useful. Better books that cover more like Shankars. –  simplicity Oct 19 '11 at 0:38
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It's absurd to say that the Feynman Lectures aren't useful - some facts in them are outdated, but you don't read Feynman for the facts. –  Mark Eichenlaub Oct 19 '11 at 2:10

This isn't especially similar to The Princeton Companion, but I think that Thorne and Blandford's Applications of Classical Physics covers those topics you mentioned well, except for the formalism of classical mechanics.

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Frank Wilczek will edit The Princeton Companion to Physics, but unfortunately the anticipated publication date is in 2018.

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