This book covers the syllabi of mathematics prescribed for M.A. and M.Sc. courses at all Indian universities. The emphasis has been laid on fundamental ideas, so that the students may grasp the subject easily. Each topic has been introduced and developed in as simple and straightforward manner as possible to be well within the comprehension of students of all categories. The subject matter of the book has been divided into eight detailed chapters. Chapter 1 begins with Hydrodynamics, Fluid and Shearing Stress and covers the whole gamut of Kinematics up to Filamentlines and Velocity Potential. Chapter 2 deals with Equations of Motion giving Langranges Equation and Cauchy Integrals among others. Chapter 3 explains Motions in Two Dimensions while Motion of Cylinders is taken up in chapter 4, divided into two parts. Irrotational Motion in Three Dimensions, i.e. Motion of a Sphere is studied in chapter 5 while the General Theory of Irrotational Motion is analysed in chapter 6. Chapter 7 deals with Vortex Motion while Waves have been given in chapter 8 explaining their kinds, motion, energy and other aspects. Additionally, a list of important formulas has been provided to help the students. The fundamental principles involved have been amply illustrated by diagrams and worked out examples so that the students may understand the methods clearly. Most of the questions provided in the book have been taken from question papers of various Indian universities set in different terminals as well as annual examinations. This will definitely facilitate systematic and thorough preparation for examinations. While the book is indispensable for postgraduate students of Mathematics, it will be highly useful to the aspirants of UPSC, State Public Service and other competitive examinations.