This is probably one of the best books one can use to refresh their fundamental knowledge. The only thing I felt the book was lacking was a couple of pages dedicated to the concept of matrix exponentials for solving systems of ODEs, especially since the groundwork for this topic was already laid out. For someone who is completely unfamiliar with these concepts beforehand, this book probably will not be the best choice. That's because explanations for one topic often reference material that appears a couple of hundred pages later. However, for those who want to quickly refresh their knowledge on the subject, it's one of the best books available, given the high quality and relative brevity of its proofs.
The use of "advanced" sets an expectation. The contents were far more of a range of high-school to mid-undergraduate than a specific look into deeper or even "advanced" mathematics.