Do you make any references or comparisons to other languages such as SAS, Stata, or SPSS in your book? Would someone who is very familiar with one of these
languages find the book helpful in transitioning to "R"?

Also, is there an assumption of familiarity with the statistical theory behind the techniques described in the book (at least on a basic level), or does the book provide an introduction?

These are good questions. In the book, I approach R as a data scientist. I thought about what it takes to successfully process, analyze and understand data, including

Accessing the data (getting the data into the application from multiple sources)

Cleaning the data (coding missing data, fixing or deleting miscoded data, transforming variables into more useful formats)

Annotating the data (in order to remember what each piece represents)

Summarizing the data (getting descriptive statistics to help characterize the data)

Visualizing the data (because a picture really is worth a thousand words)

Modeling the data (uncovering relationships and testing hypotheses)

Preparing the results (creating publication quality tables and graphs)

Then I tried to explain how to use R to accomplish each of these tasks.

I don't mention SAS, SPSS, and Stata explicitly, but since these are the same tasks you would use in each of these programs, the organization and topics should make immediate sense to users of those packages.

With regard to necessary background, here is the description from the preamble (the important point is in blue):

"R in Action" provides you with a guided introduction to R, giving you a 2,000 foot view of the platform and its capabilities. It will introduce you to the most important functions in the base installation and more than 90 of the most useful contributed packages. Throughout the book, our goal is practical application - how can we make sense of our data and communicate that understanding to others. When you finish, you should have a good grasp of how R works and what it can do, and where you can go to learn more. You will be able to apply a wide variety of techniques for visualizing data, and you will have the skills to tackle both basic and advanced data analytic problems.

Users without a statistical background, who want to use R to manipulate, summarize, and graph data should find chapters 1-6, 11, and 16 easily accessible. Chapter 7 and 10 assume a one semester course in statistics, while chapters 8, 9, 12-15 would benefit from 2 semesters of statistics. However, I have tried to write each chapter in such a way that both beginning and expert data analysts will find something interesting and useful.

It seems that R has multiple advantages over SAS, Stata, SPSS. It's free, has growing mindshare, actively developed, etc.
Besides existing legacy environments what can other environments offer that is really compelling?