pgAdmin 4 is usually named just pgAdmin. The "4" at the end has a long history, but isn't that important. It is not the release level; the release level at the time of writing this book is 3.0. pgAdmin 4 replaces the earlier pgAdmin 3.
When you start pgAdmin, you will be prompted to register a new server.
Give your server a name on the General tab, then click Connection and fill in the five basic connection parameters, as well as the other information. You should uncheck the Save password? box:
If you have many database servers, you can group them together. I suggest keeping any replicated servers together in the same Server ...