In traditional Chinese medicine (TCM), acupuncture has been used to heal various diseases and physiologic malfunctions in clinical practice for more than 2500 years. Due to its efficacy, acupuncture has been recommended by the World Health Organization in 1980 as an effective alternative therapy for 43 different disorders. Over the past few decades, various theories of the meridian system and acupuncture mechanisms have been proposed to explain how acupuncture might work. Most of those theories, however, cannot yet explain conclusively why acupuncture can be so efficacious in treating so many different diseases. The objectives of this course are twofold. First, we will review the current theories of meridian system. To establish a mathematically rigorous framework of TCM, the chaotic wave theory of fractal continuum is proposed. This theory is applied to characterize the essence of the meridian system. Secondly, based on the meridian system, mechanisms of acupuncture analgesia and acupuncture therapies will be investigated. It is sincerely hoped that this course can promote a true understanding of the meridian system and acupuncture mechanisms to help practitioners of acupuncture of California in treating patients in a more compassionate way.