  A group theoretical description of basic discrete symmetries (space inversion
P, time reversal T and charge conjugation C) is given. Discrete subgroups of
orthogonal groups of multidimensional spaces over the fields of real and
complex numbers are considered in terms of fundamental automorphisms of
Clifford algebras. In accordance with a division ring structure, a complete
classification of automorphism groups is established for the Clifford algebras
over the fields of real and complex numbers. Finite-dimensional representations
of the proper orthochronous Lorentz group are studied in terms of spinor
representations of the Clifford algebras. Real, complex, quaternionic and
octonionic representations of the Lorentz group are considered. The
Atiayh-Bott-Shapiro periodicity is defined on the Lorentz group. Quotient
representations of the Lorentz group are introduced. It is shown that quotient
representations are the most suitable for description of massless physical
fields. An algebraic construction of basic physical fields is presented.
