This first systematic account of the basic theory of normed algebras without assuming associativity includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This first volume focuses on the non-associative generalizations of (associative) C*-algebras provided by the so-called non-associative GelfandâNaimark and VidavâPalmer theorems which give rise to alternative C*-algebras and non-commutative JB*-algebras respectively. The relationship between non-commutative JB*-algebras and JB*-triples is also fully discussed. The second volume covers Zel'manov's celebrated work in Jordan theory to derive classification theorems for non-commutative JB*-algebras and JB*-triples as well as other topics. The book interweaves pure algebra geometry of normed spaces and complex analysis and includes a wealth of historical comments background material examples and exercises. The authors also provide an extensive bibliography. Language: English