Abstract: Container shipping lines operate worldwide networks under a fixed schedule, just like railway companies and airlines. With an increasing ship size and containerization the costs to transport goods through these networks have been lowered substantially over time and hence these networks have been a main driver behind globalization. In this lecture we present mathematical models to design and analyze such a network for a given cargo demand matrix. In such a network one has to specify the line structure, the transshipment ports, the ship type, the ship speed and the call frequency, which makes it very complex. The line structure consists of a cyclic list of ports to be visited by a ship in course of time. As the total number of ports worldwide is very large (over 100) it will be clear that there are a lot of combinations possible. The shipping line network problem is therefore more complex than the airline network problem, where planes fly often back and forth to a hub. Accordingly only in the last decade mathematical formulations have appeared for liner shipping networks. We will give an illustration of the methods for the case of connecting Indonesian ports. Finally we also list a number of open problems, like incorporating transit time in the demand function, treating networks under competition and demand uncertainty.