The stable level of the API is a tested, production-ready software. The version name in the stable API will be vX where X is an integer number, such as v1 for example.
Kubernetes API utilizes a concept of API groups. API groups have been introduced to make it easier to extend the Kubernetes API in the future. The API group is specified in a REST path and in the apiVersion field of a call's JSON payload. Currently, there are several API groups in use: core, batch, and extensions. The group name is a part of the REST path of an API call: /apis/$GROUP_NAME/$VERSION. The core group is an exception, it does not show up in the REST path, for example: /api/v1. You can find the full list of supported API groups in the Kubernetes API reference. ...
