These are the proceedings of the “International Conference of Algebra“ (Tainan, March 2005) held in memory of the distinguished Russian mathematician Kostia Beidar. 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 those branches of algebra and logic where 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; the theory of prime rings and strongly prime modules; 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 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.