This book treats: - spectral theory of Banach *-algebras, - basic
representation theory of normed *-algebras, - spectral theory of
representations of commutative *-algebras. A novel feature of the book is the
construction of the enveloping C*-algebra of a general normed *-algebra.
We give a spectral theorem for unital representions of Hermitian commutative
unital *-algebras by possibly unbounded operators in a pre-Hilbert space. A
more general result is known for the case in which the *-algebra is countably
generated.