The code here was adapted from the kotlin-sdk and typescript-sdk.
See also https://modelcontextprotocol.io/introduction
When creating a Client, list it's capabilities, and then client.Connect(transport) connects to the Transport (through Protocol which it extends) and starts the initialize process.
You can then call client.ListTools(), CallTool() etc.
Creating a Server is similar to creating a Client - define its capabilities and call server.Connect(transport) and it will start listening for messages through the Transport.
The Transport classes and Protocol are independant of MCP and could also be used for LSP client/servers etc.
The Transport class and it's client/server implementations for stdio, sse, in_memory know nothing about MCP. The role of the Transport interface is to simply send/receive JSON RPC messages, it does not format/parse messages, that's the role of Protocol.
The Protocol class is provided for formatting and parsing JSON into Request/Response/Notification/Error messages and delegates the send/receive to Transport.