Upvote:12
You will only go through immigration on your first entry to Schengen. As a visitor, you can almost regard Schengen as a single country. Rather like going between states in the USA or provinces in Canada.
However, watch out for a few things.
A trip through a non-Schengen country e.g. a flight with a change in the UK.
Not all EU countries are in Schengen e.g. Ireland.
You might encounter an ID check even within a country so carry your ID.