To provide a heat exchanger being excellent in productivity and, besides, in heat exchange efficiency and to provide a manufacture enabling sure attainment of this heat exchanger.

This heat exchanger is so constructed that a flame is passed through an inside space of a cylindrical body 1 and that heat exchange is conducted between the flame and a medium flowing through a medium passage 2 positioned outside the cylindrical body 1. In this case, a large number of through holes 21 are molded in juxtaposition outside the cylindrical body 1 monolithically with this body and the medium passage 2 is constructed of the through holes 21 of which the adjacent ones are connected by U-shaped pipes 22 so that all of the through holes 21 are put in communication.