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Ten chapters discuss the skew field of quaternions; elements of the geometry of S3, Hopf bundles, and spin representations; internal variables of singularity free vector
fields in a Euclidean space; isomorphism classes, Chern classes, and homotopy classes of singularity free vector
fields in 3-space; Heisenberg algebras, Heisenberg groups, Minkowski metrics, Jordan algebras, and special linear groups; the Heisenbreg group and natural C*-algebras of a vector field in 3-space; the Schrodinger representation and the metaplectic representation; the Heisenberg group as a basic geometric background of signal analysis and geometric optics; quantization of quadratic polynomials; and field theoretic Weyl quantization of a vector field in 3-space.
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