The work aims to provide a comparative study of various procedures that define the Element-free Galerkin method(EFGM) and the modifications or alterations that took place to improve the workability of EFGM. Every part of EFG process has been described in a different chapter and conclusions are provided in the end to help readers comprehend the improvements and alterations in the process. The book covers all the important literature works related to the analysis of fracture problems using EFGM.