The source code is, of course, the actual engine parts of this project. After all, it is a software project.
curl and libcurl are written in C.
Hosting and download
You can always find the source code for the latest curl and libcurl release on the official curl website curl.se. There are also checksums and digital signatures provided to help you verify that what ends up on your local system when you download the files, are the same bytes in the same order as were originally uploaded there by the curl team.
If you would rather work directly with the curl source code off the source code repository, you find all details in the curl GitHub repository.
Clone the code
git clone https://github.com/curl/curl.git
This gets the latest curl code downloaded and unpacked in a directory on your local system.