But statistical learning focuses more on functional approximation of data. I think this MIT course on statistical learning theory provides more in-depth discussion on the topics. 

If you look at the structure of the lectures, you will find that it is quite different from the structure of the lectures from the Machine learning course. 

Again, I think just reading the textbook or the lecture notes probably is not enough. You probably want to run some codes on some examples by yourself. Perhaps you can run various algorithms within R software or others such as Matlab.

If the data domain is continuous, the techniques to be applied should be statistical. Statistical learning techniques are more traditional. These techniques can be thought of functional approximation techniques as pointed out in the lecture notes in the MIT statistical learning theory course.

In order to understand the statistical learning techniques, it is helpful to understand various optimization methods. To learn optimization methods, you probably want to download and read this great book on Convex optimization from Stanford. To understand various optimization techniques, you probably also need to refresh the knowledge in Linear Algebra and Matrix operation. You can reference and download this great book on Matrix.

The field of statistical learning is rich. When speaking about statistical learning theory, most people would refer to the book The Nature of Statistical Learning Theory by Vladimir N. Vapnik. I do have this book if you want to take a look. But I think it is not easy to understand the book. Vapnik is the famous guy who brought up the concept of VC dimension and kernel machine.

I think it is much easier to read the book The Elements of Statistical Learning, by T. Hastie, R. Tibshirani, J. H. Friedman. It may be easier to download and read the book by David Mackay.