This is the proceedings of the “International Conference of Algebra” held in memory of the distinguished Russian mathematician Kostia Beidar in Tainan in March 2005. The volume consists of seven survey papers written by leading experts in the area (and Beidar's co-authors) that present the current status of the branches of algebra and logic in which Beidar made fundamental contributions. These include the theory of functional identities and its applications to Lie maps and the solution of the Hernstein Conjectures, the theory of orthogonal completions and its applications to semiprime rings, and the theory of prime rings and strongly prime modules. Also presented are the deep results of Beidar on near-rings and radical theory, Hopf algebras, and the (still open) separativity problem for von Neumann regular rings. Finally, a list of all Beidar's publications (divided into sections by subject) is presented. All the survey papers are written very carefully and will thus be of great help both for researchers and graduate students working in the related areas of algebra and logic.