Microsoft and cross-platform?! Sounds like an oxymoron. Yet the book shows how .NET has given rise to this. The key step was Microsoft transferring the specifications of C# and .NET's CLI to ECMA and ISO. This lets third parties write compilers that produce IL bytecode and thence to assembly in a given hardware.
So you could write C# code on some platform, like linux. Then with Mono or Portable.NET, produce x86 binaries.
The authors describe the open source Mono and Portable, and compare these with Microsoft's own .NET offerings. They show that Mono and Portable are quite functional. For example, using Portable, you can write in Java, C#, C or VB.NET and compile.
The book goes into some moderate level of detail about CLI. But if you are a programmer in C# or C, say, and you just want to get native binaries, without wanting to know about CLI, the book is still useful. You can safely skip the CLI sections, without losing the gist of what you need to know. For many of us, whatever language we use, we don't need or want knowledge of a specific assembly language.