We have Weyl, Pauli, Dirac and Cartan to thank for our modern

theory of groups in physics. This book published in 1937

has none of the later Lie algebra representations of the Cartan generalization of groups

and thus, like Weyl's similar book may deceive the reader into thinking

he understands when he has only a rough and not very even

introduction to these groups. This book doesn't reach much higher than SU(2),

SO(3) and the Dirac U(1)*SU(2)*SU(2).

The standard model of physics deals with the symmetry breaking of SU(5)

( the Cartan A_4 group) to U(1)*SU(2)*SU(3). The Lie algebras and

irreducible Cartan representations of such higher symmetries

will demand the student read further than this text.

So this book is an historical introduction that gives the starting basis

for the mathematics needed by modern students in physics and chemistry.