Spherical Trigonometry deals with triangles drawn on a sphere. The subject originated in the Islamic Caliphates of the Middle East, North Africa and Spain during the 8th to 14th centuries. The development of this subject lead to improvements in the art of navigation, stellar map making, geographic map making, the positions of sunrise and sunset, and improvements to the sundial. On the surface of a sphere, the closest analogue to straight lines are great circles, i.e. circles whose centres coincide with the centre of the sphere. Spherical astronomy is the branch of astronomy that is concerned with where celestial objects are located and how they move on the celestial sphere. It is one of the oldest fields of the astronomical science. If you go out in an open field on a clear night and look at the sky, you have no indication of the distance to the objects you see. A particular bright dot may be a airplane a few miles off, a satellite a few hundred miles off, a planet a many millions of miles away, or a star more than a million times further away than the most distant planet. Since you can only tell direction you can imagine that the stars that you see are attached to the inside of a spherical shell that surrounds the Earth. The present book is divided into two sections i.e. Spherical Trigonometry and Spherical Astronomy. This book has been written by keeping in view the syllabi of several universities and colleges along with the new pattern of UGC. The textbook gives a general but comprehensive introduction to the subjects to make it useful not only to the students but also as background reference book for research scholars and other professionals in the field.