There are several worthwhile books on Taijiquan. A few on philosophy and background are included at the bottom. Taiji cannot be learned from books, however they can be useful references.
Lo, Benjamin Pang Jeng; Inn, Martin; Amacker, Robert; and Foe, Susan. (1979) The Essence of T’ai Chi Ch’uan: The Literary Tradition.Richmond, California: North Atlantic Books. The Classics of Taiji. If you own only one book on Taijiquan it should be this one.
Cheng Man Ch’ing. (1985) Cheng Tzu’s Thirteen Treatises on T’ai Chi Ch’uan. Translated by Benjamin Pang Jeng Lo and Martin Inn. Berkeley, California: North Atlantic Books. Prof. Cheng’s best book on Tatji. If you own only two, this should be the second.
Yang Chengfu. (2005) The Essence and Applications of Taijiquan. Translated by Louis Swaim. Berkeley, California: North Atlantic Books. Ghostwritten by Prof. Cheng and includes a forward by him.
Chen Wei-Ming. (1985) T’ai Chi Ch’uan Ta Wen: Questions and Answers on T’ai Chi Ch’uan. Translated by Benjamin Pang Jeng Lo and Robert W. Smith. Berkeley, California: North Atlantic Books. Questions answered by Yang Cheng-fu.
Wile, Douglas. Translation. (1983) T’aichi Touchstones: Yang Family Secret Transmissions.Brooklyn, New York: Sweet Ch’i Press. Translation of many documents from the Yang Family.
Davis, Barbara. Translator. (2004) The Taijiquan Classics, an Annotated Translation Including a Commentary by Chen Weiming. Berkeley, California: North atlantic Books. A scholarly examination of the Taiji Classics.
Jou Tsung Hwa. (1980) The Tao of Tai-Chi Chuan. Rutland, Vermont; Charles E. Tuttle Co.
Pang, T.Y. (1987) On Tai Chi Chuan. Bellingham, Washington: Azalea Press.
Smith, Robert W. (1974) Chinese Boxing: Masters and Methods. New York, New York: Kodansha International. An overview of several martial artists, including Prof. Cheng.
Breslow, Arieh Lev. (1995) Beyond the Closed Door, Chinese Culture and the Creation ofT’ai Chi Ch’uan. Jerusalem, Israel: The Almond Blossom Press. An historical look at the many philosophical streams that converged in the making of Taiji.
Chan, Wing-sat. (1963) A Source Book in Chinese Philosophy. Princeton, New Jersey: Princeton University Press. Several chapters on Confucius.
Gibbs, Tam C. Translation. (1981) Lao-Tzu: “My Words are Very Easy to Understand.” Lectures on the Tao Teh Ching by Man-jan Cheng (Cheng Man-ch’ing). Berkeley, California: North Atlantic Books. An excellent translation.
Wilhelm, Richard and Baynes, Cary F. Translators. (1950) The I Ching or Book of Changes. New York, New York: Bollingen Foundation, Inc. The foundation of Chinese culture, as well as the art of Taiji.
Sun Tzu. (1988) The Art of War. Translated by Thomas Cleary. Boston, Massachusetts: Shambhala Publications, Ltd. Martial strategy.
Kaptchuk, Ted J. (1983) The Web That Has No Weaver, Understanding Chinese Medicine. Chicago, Illinois: Congdon & Weed, Inc. A comprehensive introduction.