This book contains the plenary lectures presented at the workshop 'Operators, Systems and Linear Algebra: Three Decades of Algebraic Systems Theory,' held in Kaiserslautern, Germany, September 24-26, 1997. It is a festschrift honoring the impact of the work of Paul Fuhrmann in operator and control theory. The book includes essays written by prominent scientists to present their views on some of the most recent developments in the area of mathematical systems theory and its applications. The papers cover a wide range of theoretical and applied topics, with emphasis on computational aspects and relations to engineering problems. The impact of Paul Fuhrmann's work can be traced through many parts of the volume. Polynomial models and shift realizations, the algebraic structure of linear state feedback, partial realization theory, and the recursive inversion of Hankel and Toeplitz operators are discussed.