'It contains a systematic presentation at the graduate level. This fact makes the book understandable for a wide audience of mathematics students and scientists. The book can be highly recommended not only tot specialists but also for beginners in the field as a first source.' Mathematical Reviews, 1986

• I: Introduction.- II: Elementary Theory of Orthomodular Lattices.- 1. Ortholattices.- 2. Commutativity.- 3. Orthomodular lattices.- 4. Properties of commutativity in orthomodular lattices.- 5. Characteristic properties of orthomodular lattices.- 6. Interval algebra.- Exercises.- III: Structure of Orthomodular Lattices.- 1. Skew operations.- 2. Free orthomodular lattice F2.- 3. Introduction to Hilbert spaces.- 4. Projection lattice of a Hilbert space.- Exercises.- IV: Amalgams.- 1. Amalgams of posets.- 2. Amalgams of lattices.- 3. Amalgams of orthomodular lattices.- 4. Atomic amalgams of Boolean algebras.- Exercises.- V: Generalized Orthomodular Lattices.- 1. Orthogonality relation.- 2. Janowitz’s embedding.- 3. Congruence relations.- 4. Congruence relations and p-ideals.- 5. Commutators.- Exercises.- VI: Solvability of Generalized Orthomodular Lattices.- 1. Reflective and coreflective congruences.- 2. Projective allelomorph.- 3. Commutator sublattices.- 4. Solvability in equational classes of lattices.- Exercises.- VII: Special Properties of Orthomodularity.- 1. Commutators of n elements.- 2. Finitely generated orthomodular lattices.- 3. Formulas for orthomodular lattices.- 4. Exchange theorems.- 5. Center of an orthomodular lattice.- 6. Identities and operations.- 7. Analogues of Foulis-Holland Theorem.- Exercises.- VIII: Application.- 1. Orthomodularity and experimental propositions.- 2. Compatibility.- 3. Dimension theory.- 4. Orthologics.- Exercises.- Answers to Exercises.- Solutions to Exercises of Chapter II.- Solutions to Exercises of Chapter III.- Solutions to Exercises of Chapter IV.- Solutions to Exercises of Chapter V.- Solutions to Exercises of Chapter VI.- Solutions to Exercises of Chapter VII.- Solutions to Exercises of Chapter VIII.- References.

'It contains a systematic presentation at the graduate level. This fact makes the book understandable for a wide audience of mathematics students and scientists. The book can be highly recommended not only tot specialists but also for beginners in the field as a first source.' Mathematical Reviews, 1986

• I: Introduction.- II: Elementary Theory of Orthomodular Lattices.- 1. Ortholattices.- 2. Commutativity.- 3. Orthomodular lattices.- 4. Properties of commutativity in orthomodular lattices.- 5. Characteristic properties of orthomodular lattices.- 6. Interval algebra.- Exercises.- III: Structure of Orthomodular Lattices.- 1. Skew operations.- 2. Free orthomodular lattice F2.- 3. Introduction to Hilbert spaces.- 4. Projection lattice of a Hilbert space.- Exercises.- IV: Amalgams.- 1. Amalgams of posets.- 2. Amalgams of lattices.- 3. Amalgams of orthomodular lattices.- 4. Atomic amalgams of Boolean algebras.- Exercises.- V: Generalized Orthomodular Lattices.- 1. Orthogonality relation.- 2. Janowitz’s embedding.- 3. Congruence relations.- 4. Congruence relations and p-ideals.- 5. Commutators.- Exercises.- VI: Solvability of Generalized Orthomodular Lattices.- 1. Reflective and coreflective congruences.- 2. Projective allelomorph.- 3. Commutator sublattices.- 4. Solvability in equational classes of lattices.- Exercises.- VII: Special Properties of Orthomodularity.- 1. Commutators of n elements.- 2. Finitely generated orthomodular lattices.- 3. Formulas for orthomodular lattices.- 4. Exchange theorems.- 5. Center of an orthomodular lattice.- 6. Identities and operations.- 7. Analogues of Foulis-Holland Theorem.- Exercises.- VIII: Application.- 1. Orthomodularity and experimental propositions.- 2. Compatibility.- 3. Dimension theory.- 4. Orthologics.- Exercises.- Answers to Exercises.- Solutions to Exercises of Chapter II.- Solutions to Exercises of Chapter III.- Solutions to Exercises of Chapter IV.- Solutions to Exercises of Chapter V.- Solutions to Exercises of Chapter VI.- Solutions to Exercises of Chapter VII.- Solutions to Exercises of Chapter VIII.- References.