Details of the API usage are described at the version-specific pages:
REST API Versions
As REST API evolves from one TeamCity version to another, there can be incompatible changes in the protocol.
http://teamcity:8111/app/rest/ URL the latest version is available.
<version> URL, other versions CAN be available. Our general policy is to supply TeamCity with ONE previous version.
In TeamCity 7.x you can use "6.0" instead of <version> to get the previous version of the protocol.
In TeamCity 8.0 you can use "6.0" or "7.0" instead of <version> to get earlier versions of the protocol.