In my goal to self study up to Calculus, I've utilized the very useful Insights page on what books are best for a real intuitive understanding in basic high school mathematics such as Algebra, Geometry, Trigonometry. I purchased all the recommended books and I was wondering what some of the differences are between some of the "subjects". To cut to the chase, what's the difference between: 1. Algebra and Abstract Algebra 2. Synthetic Geometry and Analytic Geometry I searched around but really all I could find was problems and books for them. I'm really just looking for a quick idea of what their differences are in a quick simple manner ie "Synthetic Geometry is about abc and Analytic Geometry is about xyz." Thank you for any help.