Dear Arivazhagan, CGM is a method for numerical resolution of systems of linear equations, which can be applied to PDE resolution after its discretization on a grid. Good references are:
Golub, Gene H.; Van Loan, Charles: Matrix computations, Chapter 10;
Quarteroni, Alfio: Numerical Models for Differential Problems, Chapter 7.
Gianluca
I would recommend Shewchucks introduction to conjugate gradient without the agonizing pain
https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf
Let me put in a shameless plug for the book "Numerical methods of scientific computing" by Guus Segal, Fred Vermolen and myself. It covers the transition from PDE to system of equations by finite element, finite volume or finite difference methods and methods of solving them, in particular Krylov methods like Conjugate Gradients and BiCGSTab and most importantly various preconditioners like incomplete LU to enhance convergence.
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