Despite Alexander’s acting and performing experience there is no discussion of acting in his books. See Stage Fright for brief references to stage fright in his writings and lectures.
The Alexander Technique was taken up by acting colleges, first in London in the 1960s, and has since been taught, either individually or in groups, at many acting colleges, predominantly in the UK and the US. Many actors use or have used the Technique. The literature is extensive.
The Alexander Technique For Actors by Kelly McEvenue contain warm-up exercises, drama exercises; it relates the Technique to voice work; and then discusses various examples of difficult acting roles, situations and environments. Kelly McEvenue works for the acting company of the Stratford Festival of Canada 
The Actor’s Secret by Betsy Polatin is an introduction to the Alexander Technique. As well as the Technique she uses Breathing Coordination and Somatic Experiencing for her exploratory exercises (which are based on her classes at the Boston University’s College of Fine Arts School of Theater faculty).
Physical Expression on Stage and Screen by Bill Connington is an introduction to the Alexander Technique with exploratory exercises (with links to 15 online videos demonstrating these). Bill Connington has taught at the New Your University’s Tisch School of the Arts, the Julliard School, the Actor Studio MFA Program, and is currently lecturing the Yale School of Drama.
Before the Curtain Opens by Kate Kelly is an introduction to the Alexander Technique, in particular focusing on how much the Technique can contribute to the preparation for performance.
Integrative Alexander Technique Practice for Performing Artists by Cathy Madden considers the processes for change, e.g. 1. wanting, 2. recognizing, 3. deciding, 4. asking, and 5. experimenting, always emphasizing the freedom of choice. Cathy Madden is lecturer for the University of Washington’s Professional Actor Training Program.
Galvanizing Performance edited by Cathy Madden, Kathleen Juhl is a collection of papers, mainly on acting, but also for musicians, singers, and dancers. The books focus is on the practical incorporation of the Technique in performance.
Touching Lives by Sue Laurie is her memoirs of teaching the Alexander Technique at the RSC 1983-2010 and at the National Theatre (London) from 1989 onwards.
The Use of the Voice by Robert Macdonald is an exposition of his thesis for his Master of Arts Degree at the Central School of Speech and Drama, London. The research involved a study of three cases and investigated the role that the Alexander Technique in changing their vocal functioning and eventual performance of Shakespearean text.
Articles – General
‘Tension and the Actor’ by Joyce Wodeman is the first article (1962) dedicated to the benefits of the Alexander Technique for the actor. Joyce Wodeman taught acting and trained as a teacher of the Technique.
‘The Alexander Technique and the actor’ by John Gray also examines the general benefits of the Technique for the actor.
‘Speaking Shakespeare’s Sonnets’ by Lawrence Bruce discusses the use of breath in speaking the sonnets.
‘Stanislavsky and the Alexander Technique’ by Nicolette Lee relates her experiences of how the Alexander Technique benefits Stanislavsky work.
In ‘The actor and the neutral state’ by Joan Diamond she argues that an actor needs to cultivate a neutral state before entering the character the actor is going to play, and that the Alexander Technique facilitates this.
Articles – Teaching actors
‘The Alexander Technique in the training of actors’ by Steven Hallmark argues for the importance of basic chair and table work for providing the acting student with the essential fundamentals for all forms of acting. Hallmark also describes some of the exercises he used for acting students in Stockholm in 1993-99.
‘What is presence on stage?’ by Penny O’Connor relates some of the processes she use to help young actors to discover their stage presence.
In ‘Preparing a role’ Joan Schirle relates how she used the Technique playing a woman in a wheelchair.
‘The use of conscious inhibition in the work of a performing artist’ reports on a study in which three musicians and three actors were tested three times over a period of two years (2006-08), before and after 20 Alexander Technique lessons, and then after a further period of six months. Both qualitative and quantitive methods were used to measure changes, and all measurements showed an improvement in performance.
The Alexander Technique – Solutions for back trouble (DVD) contain an interview with William Hurt on the benefits of the Alexander Technique.
See also Voice, Delsarte, Stage Fright.