Are there any terse, accessible books that are geared specifically at learning these two formalisms and how to effectively use them? So far I've only see either topic introduced as a part of another book, like QM or classical mechanics. I was hoping for something focused more or less exclusively on these formulations that would then go on to explain important nuances and limitations, and then systematically show how to apply them effectively.
I have finished reading a great book called "The Theoretical Minimum" by Leonard Susskind (a famous string theorist) and George Hrabovsky. It's about classical mechanics but mainly talks about both the Lagrangian formulation and the Hamiltonian formulation of classical mechanics. It is great for beginners in physics or just about anyone. It also reviews the differential, integral, and multivariable calculus needed for understanding these topics. It also gives some examples on how to use both formulations. Oh, and also, at the beginning of each chapter, there is a fun short story!