Get ready . . . AH-EPS does NOT (by design) do everything! What it does it does exceedingly well, however. It focuses on integrated teaching and change, real time interaction between instructor and student: how to talk and anchor change in class, live.
In some cases and classes it may need to be complemented or expanded upon. ("Compliments," it always has lots of!) Here are my three recommendations, what you should have either on your bookshelf or bookmarked:
Well Said by Linda Grant
For more detailed explanation and academic application, especially for more advanced students, use Grant.
Clear Speech and Clear Speech from the Start by Judy Gilbert
For colourful visual models, related listening comprehension training and communicative pair work, use Gilbert.
Accent Coach and its mobile app by Ron Thomson
For more focused, personalized drill and effective repetition after haptic vowel work, use Thomson.
AH-EPS haptic video work (in 30-minute weekly lessons with optional homework) presents the English sound system as a whole and teaches students a set of gesture-based procedures that they and their instructor can use every day in modelling and correcting pronunciation. (There are additional video lessons with each module for students to practice on their own, if their instructor does attend to pronunciation in regular speaking and listening instruction.)
It is generally adaptable to any proficiency level, any age learner or amount of instructor experience in pronunciation teaching. If, however, you only have time or money to go with one system, I'd still recommend this for starters: