The field of mathematics that focuses on the relationship between angles and side lengths of triangles is known as trigonometry. The real functions that relates an angle of the right-angled triangle with the ratios of the two side lengths are known as trigonometric functions. This field is known for its triangle and trigonometric identities, which are used to solve complex equations and find new relationships. Some of the triangle identities are law of sines, cosines and tangents whereas Pythagorean identities and Euler's formula are some of the trigonometric identities. This field finds its applications in the fields of optics, acoustics, astronomy, celestial mechanics, periodic functions, navigation, surveying, phonetics, geodesy, architecture, economics, computer graphics, crystallography, electrical engineering, biology and medical imaging. This book is a valuable compilation of topics, ranging from the basic to the most complex theories and principles related to this discipline. Different approaches, evaluations, methodologies and advanced studies related to this field have been included in this book. Through this book, we attempt to further enlighten the readers about the new concepts in trigonometry.