This paper is intended to be an introduction to the field of abstract interpretation of logic programs. Abstract interpretation can be thought of as providing a new (or abstract) semantics for the language under consideration and then showing how the meaning of a program in the new semantics is an abstraction of the meaning of the program in standard semantics. We discuss the issues involved in deriving an abstract interpretation scheme and present an efficient and domain-independent algorithm for computing fixed points in the context of abstract interpretation of logic programs. A brief introduction to denotational semantics is also provided in order to make the paper self-contained.