Lamorna's Beginner Clarinet Book" is now my (and my students) favourite tutor book for those commencing their clarinet studies. The structure of the book is clear and well paced, with lots of tips on clari technique and counting skills. The book starts with how to make a sound, and progresses to a brief introduction to the upper register and compound time.
Each new note or concept is supplemented by an abundance of tunes and duets. My students particularly like the quizzes and report cards at the end of each chapter, theory tasks, the occasional improvisation activity, and of course the plethora of duets.
This book presents the material in a fun and engaging way, while still enforcing all the basic concepts. Try it - you won't look back.