The main documentation is sub divided into several categories. Each category holds a number of documentation pages.
The book: Everything curl
This is a detailed and totally free book, available online (and as a PDF as a link from there) that explains everything there is to know about curl, libcurl and the associated project.
Learn how to use curl. How to use libcurl. How to build them from source or perhaps how the curl project accepts contributions. There's something for everyone in this, from the casual first-time users to the experienced libcurl hackers.
The libcurl sub section of the site is huge!
Plenty of documentation and details if you want to work on curl or libcurl themselves.