This book provides the necessary background of geometry, mathematics and
physical geodesy, useful to a rigorous approach to geodetic heights. The
concept of height seems to be intuitive and immediate, but on the
contrary it requires a good deal of scientific sharpness in the
definition and use. As a matter of fact the geodetic, geographic and
engineering practice has introduced many different heights to describe
our Earth physical reality in terms of spatial position of points and
surfaces. This has urged us to achieve a standard capability of
transforming one system into the other. Often this is done in an
approximate and clumsy way. This book solves the above practical
problems in a rigorous way, showing what degree of approximation is used
in approximate formulas. In addition the book gives a sound view on a
matter that is presently occupying scientific associations, namely the
unification of the global and regional height reference systems. It
provides the mathematical background as well as the state of the art of
its implementation. It will be particularly useful for professionals and
national agencies.