I zoomed the first easier chapters of the classical mechanics, the classical field theory, and the non-relativistic quantum mechanics. These materials are everywhere including the scattering theory (the so-called S-matrix theory and the related algebraic analysis [D-modules] of the RIMS, Kyoto).
However, the materials treated in the Landau textbooks are obsolete in a sense. I mean, the quantum electro-dynamics (QED) is not well-described in the Landau course -- the Feynman diagram does not have a standard space-time axes and the [single / double] arrows of the modern theoretical physics after 't Hooft. Landau abandoned the quantum field theory at his later years.
Apart from the advanced materials of (quantum) statistical physics / stochastic calculus [not always the condensed matter physics for the applied engineering and high-temperature superconductivity], we can see some of better modern textbooks. It is like Bourbaki. Bourbaki was a classic and it was written at the highest level at those ages, but now we have better textbooks and we can understand the curriculum more easily.
Although the fluid mechanics of the 19th century (well, I don't want to talk much about the plasma physics) and the elastic theory are not well inherited, we have the books of "[the] Ginzburg-Landau Equations and Stability Analysis" [Iwanami Press, still no English translation available] by Shuichi Jimbo and Yoshihisa Morita [ISBN=978-4000075619] and "An Introduction to Quantum Field Theory" by Michael E. Peskin and Daniel V. Schroeder. [ISBN=978-0201503975]
I read the Peskin-Schroeder at the junior and senior [the 3rd and 4th year of the UTokyo, the academic year 2000-2001]. I performed the Peskin-Takeuchi's "Physics beyond the standard model" [phenomenology of elementary particle theory including muons [leptons: the anomalous magnetic moment g-2] & (Yukawa's) pions [pi mesons of quarks decayed to multiple photons: chiral abelian anomaly and the Riemann-Roch-like theorem of Fujikawa's method by chiral fermions] but without any sound mathematical foundation] at the 1st year summer seminar of my master's period.
Peskin seminar was after the seminar of "Renormalization: An Introduction" by Manfred Salmhofer [Springer, ISBN=978-3642084300] during the winter holidays [a little before 2002-March] with the theoretical physics students working on the condensed matter physics. I didn't sufficiently understand the Fermi surface problem [still a mystery in the AdS/CFT correspondence conjecture] at those days, which is not treated in the renormalization group theory in the quantum field theory of the elementary particle theory.
To sum up, the Feynman rules [including the statistical factors of second quantization of Bose-Einstein / Fermi-Dirac statistics of identical particles] for the perturbative [asymptotic series of] Feynman integrals [as well as symmetry breakings after the late Yoichiro Nambu, the phase transition theory, and some of the so-called standard model] are treated more shortly in the textbook of Peskin-Schroeder. Non-perturbative effects of solitons, supersymmeties, and D-branes / M-branes [of the so-called superstring theory, which I still doubt in the effectiveness to the real-world problems] are not treated in this pedagogical textbook.
I still think Peskin is worthy of attention for undergraduate physics students and determined mathematical physicists [including mirror symmetrists and twistor theorists among other geometric representation theorists at the math department]. Of course, I mentioned no classic literature of quantum field theories including Zinn-Justin and Bjorken-Drell. Ryder [ISBN=978-0521478144] might be a second choise and available on the web.