The classic traveling salesman problem asks us to find the shortest route that that goes through each of a given set of cities precisely once before returning to the initiail city. If A, B and C are any three cities, the distance from A to C is always shorter than the sum of the distances from A to B and then from B to C. This is known as the triangle inequality. The general traveling salesman problem is obtained when the triangle inequality is not required. This would be the case when we place arbitrary positive numbers in an n X n matrix and, starting with the first row, we attempt to obtain the shortest or nearly shortest route going through each row number exactly once before returning to the first row number. Such a route is called a tour.This book provides original algorithms for the symmetric, asymmetric, bottleneck and multiple traveling salesman problems. It also contains one for the traveling purchaser problem and three for the multiple traveling purchaser problem. A large example of the asymmetric TSP has been added to chapter 3. Theorems 7.1-7.4 improve many of the algorithms in the book. For resellers, please contact CreateSpace Direct.