I'm looking for an overview of the history of Europe since the Renaissance. I found this book on Amazon: A History of Modern Europe: From the Renaissance to the Present by John Merriman Ph.D. An older edition from 2004 is available for a cheap price. Do history textbooks change much over different editions?
It depends.
In terms of general content, the variation between editions of the same textbook can be there but not noticeable. For example, some history textbook editions might add in a new chapter to better fit a certain theme. This can be reflective of broader changes within the academy and focus on historians. A hypothetical textbook on American culture written in the 1980s might not have much on LGBTQ history, but one written after the millennium could have more of this material because the field of LGBTQ studies is much wider and developed than in earlier decades. By the same token, newer editions sometimes approach topics differently or with different emphasis. But a lot of history textbooks still try and cover major events and people. Big events and people (eg the Thirty Years' War, Martin Luther, Hitler) will probably be covered throughout different editions of textbooks and the nature of textbooks ("a mile wide and an inch deep" is how a colleague described them) means that there won't be too much variation with the big things.
There is of course one crucial difference between textbook editions. Textbooks are meant for classroom instruction and there often is a variation between various classroom exercises such as discussion questions, primary sources, or identification terms. While a number of jaded students think that this is a ploy by textbook companies to keep grinding out new editions, the different drills and exercises are supposed to reflect proper pedagogy. That means they should reflect current theories on learning. So even if historians' assessments of big stuff has not changed that much between decades, the pedagogical methods used to teach certainly have changed. There are more than a few students in history classes who believe that saving money on an older edition is a smart move but discover they cannot fully complete the course or have to do extra work to fill in the gaps between the current and older edition.
So if you're reading an older edition of A History of Modern Europe: From the Renaissance to the Present for your own edification and learning, the differences might not matter. But if you're doing so to save a few bucks on a class and use the price differences for beer money, caveat emptor.