1 Definitions. - A. Metric spaces. -B. Topology. - C. Variations. -D.

Maximal metric and gluing. - E. Completeness. -F. Compact spaces. - G. Proper spaces. -H.

Geodesics. - I. Metric trees. - J. Length. - K. Length spaces. - 2 Universal spaces.

- A. Embedding in a normed space. - B. Extension property. - C. Universality. - D. Uniqueness and homogeneity.

- E. Remarks. - 3 Injective spaces. - A. Definition. - B. Admissible and extremal functions. - C.

Equivalent conditions. - D. Space of extremal functions. - E. Injective envelope. - F. Remarks. - 4 Space of subsets.

- A. Hausdorff distance. -B. Hausdorff convergence. - C. An application. -D. Remarks.

- 5 Space of spaces. - A. Gromov-Hausdorff metric. - B. Approximations and almost isometries 49; C. Optimal realization 50; D. Convergence 51; E. Uniformly totally bonded families 52; F.

Gromov selection theorem. - G. Universal ambient space. - H. Remarks. - 6 Ultralimits. - A. Faces of ultrafilters.

- B. Ultralimits of points. - C. An illustration. - D. Ultralimits of spaces. - E. Ultrapower.

- F. Tangent and asymptotic spaces. - G. Remarks. - Semisolutions. -Index. - Bibliography.