Are there API's available by default to interact with a standard online store client?

Hi,

We have a video platform with an interaction layer. Our customers embed our platform on their websites.
We are looking for ways to embed our platform (liveryvideo.com) to the Shopify Online store. Users should be able to add products to a shopping basket in our embedded interaction layer to the underlying default online store. Are there API’s available by default to interact with an online store?

Thanks in advance,
Paul van Beukering