On quaternions and octonions: their geometry, arithmetic, and symmetry

This books gives a window into the newer notation in group theory.Sometimes things that are "obvious" to Conway and his co-arthor,just aren't to the rest of us.But in contrast to that he gives concrete examplesof new approaches that are beyond classical Coexterand Cartan type approaches.If you are looking for physics applications to quantum mechanicsfor modern group theory,you might want to try another book,but if you want an idea of what a Moufang loop is or why octonions are not associative, then you might like this book.Some time in this century we may even geta chance to understand Freudenthal's metasymplectic geometry?This book for me is sort of a study guide towhat i should try to learn for the future?