Standard Integral Table Algebras Generated by Non real Element of Small Degree Introduction (Z. Arad M. Muzychuk): Main Definitions; Basic Examples; Basic Properties Basic Constructions ITA with a Faithful Nonreal Element of Degree 4 (Z. Arad M. Muzychuk H. Arisha E. Fishman): Known Examples; Proof of the Main Results SITA with a Faithful Nonreal Element of Degree 5 (Z. Arad F. Bünger E. Fishman M. Muzuychuk): Introduction; General Facts and Known Results; Degree 5; Case 3; Case 5 SITA with a Faithful Real Element of Degree 5 and Width 3 (F. Bünger): Introduction; Case 1; Case 2 The Enumeration of Primitive Commutative Association Schemes (M. Hirasaka): Introduction; The Case of Valency 1 or 2; The Case of Valency 3; The Case of Valency 4 References Index.