This book presents methods of studying transonic flows applicable to various astrophysical circumstances. This is the first book of its kind and efforts have been made to be as thorough as possible. It gives complete mathematical solutions for the study in this area including various shock transitions. For any theoretical astrophysicists this book is expected to be very useful as the formalism discussed can be applied to all the branches. Both axisymmetric and non-axisymmetric flows are studied.