This book has grown out of my research interests in the theory of oper-
ator algebras, orthomodular structures and mathematical foundations of
quantum theory. It is based on a series of lectures on measure theory on
nonboolean operator structures which I prepared for Ph. D. students in
Workshops on Measure Theory and Real Analysis in Italy (Gorizia 1999,
Grado 2001) and which I have delivered at the conferences of the
Interna- tional Quantum Structures Association in Berlin 1996, Cesena
2001, and Vienna 2002. I have worked on these subjects in the framework
of Prague's Semi- nar on Mathematical Formalism of Quantum Theory
founded by P. Ptak. Many results presented in the book were also
obtained during my longer research stays abroad, in particular at the
Department of Mathematics, Reading University, U. K. (1993) and at the
Mathematical Institute of Er- langen University, Germany (1996-1997,
2000 and 2003). Both the research activity and the work on the book was
supported by a few international projects I participated in. I would
like to acknowledge the support of European Community that supported my
research stay in Reading University (Grant COST, Noncommutative Measure
Theory and von Neumann Algebras, 1993). I am also very much grateful to
the Alexan- der von Humboldt Foundation, Bonn, for long-term support of
my research and for awarding me the grants that enabled me work at
Erlangen Uni- versity in 1996-1997, 2000 and 2003.
