Topics include: 1. Free independence and non-commutative probability spaces; 2. R-transform and S-transform in free probability; 3. Free central limit theorem and free convolution; 4. Combinatorics of non-crossing partitions; 5. Random matrix models and their connection to free probability; 6. Asymptotic eigenvalue distributions of random matrix ensembles. Students should seek approval from the course instructor to take this course.