I: Differential-Geometrical Structures on Manifolds.- 1. Linear connections on a manifold.- 2. The Levi-Civita connection.- 3. Submanifolds of a Riemannian manifold.- 4. Distributions on a manifold.- 5. Kaehlerian manifolds.- 6. Sasakian manifolds.- 7. Quaternion Kaehlerian manifolds.- II: CR-Submanifolds of Almost Hermitian Manifolds.- 1. CR-submanifolds and CR-structures.- 2. Integrability of distributions on a CR-submanifold.- 3. ?-connections on a CR-submanifold and CR-products of almost Hermitian manifolds.- 4. The non-existence of CR-products in S6.- III: CR-Submanifolds of Kaehlerian Manifolds.- 1. Integrability of distributions and geometry of leaves.- 2. Umbilical CR-submanifolds of Kaehlerian manifolds.- 3. Normal CR-submanifolds of Kaehlerian manifolds.- 4. Normal anti-holomorphic submanif olds of Kaehlerian manifolds.- 5. CR-products in Kaehlerian manifolds.- 6. Sasakian anti-holomorphic submanifolds of Kaehlerian manifolds.- 7. Cohomology of CR-submanifolds.- IV: CR-Submanifolds of Complex Space Forms.- 1. Characterization of CR-submanifolds in complex space forms.- 2. Riemannian fibre bundles and anti-holomorphic submanifolds of CPn.- 3. CR-products of complex space forms.- 4. Mixed foliate CR-submanifolds of complex space forms.- 5. CR-submanifolds with semi-flat normal connection.- 6. Pinching theorems for sectional curvatures of CR-submanifolds.- V: Extensions of CR-Structures to Other Geometrical Structures.- 1. Semi-invariant submanifolds of Sasakian manifolds.- 2. Semi-invariant products of Sasakian manifolds.- 3. Semi-invariant submanifolds with flat normal connection.- 4. Generic submanifolds of Kaehlerian manifolds.- 5. QR-submanifolds of quaternion Kaehlerian manifolds.- 6. Totally umbilical and toally geodesic QR-submanifolds of quaternion Kaehlerian manifolds.- VI: CR-Structures and Pseudo-Conformal Mappings.- 1. CR-manifolds and f-structures with complemented frames.- 2. Generic submanifolds of complex manifolds.- 3. Anti-holomorphic submanifolds of complex manifolds.- 4. Pseudo-conformal mappings.- VII: CR-Structures and Relativity.- 1. Geometrical Structures of space-time.- 2. The twistor space and Penrose correspondence.- 3. Physical interpretations of CR-structures.- References.- Author Index.