This paper is an overview of the classic travelling salesman problem, and selected algorithms and heuristics that solve the problem. Four algorithms or heuristics are presented. They were chosen because of their diverse modes of attack and their implications for efficiency. Two of the algorithms are exact: an exhaustive approach and a dynamic programming approach. The other two are heuristics (approximate algorithms): the nearest neighbour approach and the nearest addition approach. The nearest insertion algorithm, which is similar to the nearest addition algorithm, is also discussed. Examples are given for each algorithm, and its worst case behaviour is analysed. Finally, there is discussion of guaranteed bounds on the costs of tours produced by the heuristics.