Free Probability Theory studies a special class of 'noncommutative'random variables, which appear in the context of operators on Hilbert spaces and in one of the large random matrices. Since its emergence in the 1980s, free probability has evolved into an established field of mathematics with strong connections to other mathematical areas, such as operator algebras, classical probability theory, random matrices, combinatorics, representation theory of symmetric groups. Free probability also connects to more applied scientific fields, such as wireless communication in electrical engineering. This 2006 book gives a self-contained and comprehensive introduction to free probability theory which has its main focus on the combinatorial aspects. The volume is designed so that it can be used as a text for an introductory course (on an advanced undergraduate or beginning graduate level), and is also well-suited for the individual study of free probability.

"This book is an absolutely indispensable resource for anyone who works in free probability theory, as well as those (advanced undergraduates or graduate students, or professional researchers) newly initiated in the field. Lectures on the Combinatorics of Free Probabilityis sure to be considered one of the important informative texts in this rapidly growing field of study, and it is highly recommended for any reader or researcher in the field."
Todd Kemp, Mathematical Reviews