Ethel's right. Ebooks from your library via the internet is in the pipeline, but it'll be a few years yet before they're widely available.
You can get older stuff to read online via Project Gutenberg, but for published, up to date stuff, you'll have to pay.
If you want to read some new, unpublished writers (like me, for instance), you could have a look
here. If my book doesn't appeal, there are loads of others, and you're welcome to join and pass comment on any of them.