Reference for Langlands functoriality conjecture view towards classical examples

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I want to know if there's any good reference on Langlands functoriality conjecture which provides connection with classical examples. What I have in my mind are followings:

  • Classical Rankin-Selberg (nice $L$-function $L(s, f\otimes g)$ built on two modular forms $f, g$) and general Rankin-Selberg $\mathrm{GL}_{n} \times \mathrm{GL}_{m} \to \mathrm{GL}_{nm}$

  • Hecke and Maass's construction of modular/Maass forms from quadratic characters (real/imaginary quadratic fields over $\mathbb{Q}$) and automorphic induction

  • Symmetric square lifting (this may corresponds to some construction of $\mathrm{GL}_{3}$ modular forms from classical modular forms, but I don't know anything about theory of $\mathrm{GL}_{3}$ automorphic forms/representations.)

  • Doi-Naganuma lifting (from ordinary modular form to Hilbert modular form) and Base change

  • Classical theta series and Howe duality stuff

Is there any good resource that contains explanation for these contents? (It would be great if there's sketches of proofs for general known cases and how the proofs for the classical version extend.)