Develop Maps

Hi gurus,

I want to start a street directory project. As I am new to algorithm design and discreet mathematics, I really have no idea how to get started? How to represent a map logically, the type of data structure to use, etc? Can somebody shed some lights, at least tell me how I can start.

Objectives of my project:
From point A to point B:
1. allows user to search for the shortest route
2. allows user to search for the fastest route, base on a fixed average speed.
3. allows user to search for the cheapest route, base on known charges for using various roads.

I am more interested in the algorithm aspect rather than the GUI aspect.
Please help...