The first Part of the thesis explains from first principles the concept of "logic programming" and its practical application in the programming language Prolog. Prolog is a simple but powerful language which encourages rapid, error-free programming and clear, readable, concise programs. The basic computational mechanism is a pattern matching process ("unification") operating on general record structures ("terms" of logic). IThe ideas are illustrated by describing in detail one sizable Prolog program which implements a simple compiler. The advantages and practicability of using Prolog for "real" compiler implementation are discussed. The second Part of the thesis describes techniques for implementing Prolog efficiently. In particular it is shown how to compile the patterns involved in the matching process into instructions of a low-level language. This idea has actually been implemented in a compiler (written in Prolog) from Prolog to DECsystem-10 assembly language. However the principles involved are explained more abstractly in terms of a "Prolog Machine". The code generated is comparable in speed with that produced by existing DEC10 Lisp compilers. Comparison is possible since pure Lisp can be viewed as a (rather restricted) subset of Prolog. It is argued that structured data objects, such as lists and trees, can be manipulated by pattern matching using a "structure 'sharing" representation as efficiently as by conventional selector and constructor functions operating on linked records in "heap" storage. Moreover the pattern matching formulation actually helps the implementor to produce a better implementation.