This Encyclopaedia is an introduction to Partial differential Equations and the relevant functional analysis tools which Partial Differential Equations require. The material intended is for graduate students of Mathematics and is based on a course that is taught in almost all Indian Universities. The purpose of the course, is to give students a rapid and solid Research-Oriented foundation in areas of partial Differential Equations. All the chapters have been organised in simple and lucid manner. The Encyclopaedia Starts with basics of differential Equation Making it Suitable for those with little background in Mathematics. The book is a is a of good size covering all the essential topics to Functions, Orthogonal Functions Laplace Transform, Infinite Series, Fourier Series, Intervals of Validity, Intervals of Validity. The Encyclopaedia focuses mainly on the Applications of Partial Differential Equation, and the Mathematical Formalism Is treated carefully but without diverging from the main objective.