Green's functions are an important tool used in solving boundary value problems associated with ordinary and partial differential equations. This self-contained and systematic introduction to Green's functions has been written with applications in mind. The material is presented in an unsophisticated and rather more practical manner than usual. Consequently advanced undergraduates and beginning postgraduate students in mathematics and the applied sciences will find this account particularly attractive. Many exercises and examples have been supplied throughout to reinforce comprehension and to increase familiarity with the technique.