Is there a nice, modern textbook (some lecture notes or survey would do, too) that covers the main results and methods from transcendence theory? Ideally, it should also have some good exercises.
So far I have been working mainly with the ($p$-adic) Subspace Theorem and I played a bit with linear forms in logarithms (in particular with Baker's theorem).
I am especially interested in the uses of continued fraction methods in transcendence proofs and in results related to Schanuel's conjecture. A quick survey of other open problems in transcendence theory would be a great bonus.