Steve Melczer has published a new text An Invitation to Analytic Combinatorics: From One to Several Variables. He characterizes the book as an “introduction to Pemantle and Wilson’s book on multivariate analytic combinatorics, aimed at a similar audience to Flajolet and Sedgewick and with more of a focus on explicit computation and worked examples”.

See his website with Sage/Maple worksheets for examples and a free copy of the manuscript.