This book is a rewrite of Lie groups and Lie algebras. The rewrite very much simplifies the standard presentations. The rewrite is done by approaching this area of physics and maths from the intuitively easy side of Lie groups first and Lie algebras second. This makes an inspiring and simple presentation of the material.

The book covers calculus in both commutative division algebras like the complex numbers and non-commutative division algebras like the quaternions. The gauge covariant derivative used in gauge theory is also covered as is the 4-dimensional space-time covariant derivative used in general relativity. The complicated Cauchy-Riemann calculus used for 200 years within the complex numbers is replaced with a simpler and much more general calculus which applies in every division algebra. This is quite revolutionary. This book is aimed at undergraduates and graduates, but it will be easily understood...