In 1661 the Royal Library (Kungl. biblioteket, abbreviated KB) was assigned the task of collecting all Swedish printed publications. Since then KB has collected, preserved and given access to an important part of our cultural and historical heritage. In the future an increasing amount of material will be published on the Internet, and only on the Internet. If the Royal Library is going to continue to fulfil its historic role, the activities must be widened to encompass also what is published electronically. In 1996 KB inaugurated a project, entitled Kulturarw³ (The Swedish Archiw³e) to address those issues. The aim of the project is to test methods of collecting, preserving and providing access to Swedish electronic documents, which are accessible on line in such a way that they can be regarded as published. Since the start of the project there have been made seven complete downloads of the Swedish web. Currently, the collection comprises about 65 million items. About half of them are text documents, mostly html and plain text. Through this project KB is also laying the foundations of a collection of Swedish electronic publishing for our time and for coming generations.