This book focuses on the phenomena of inertia and gravitation one objective being to shed some
new light on the basic laws of gravitational interaction and the fundamental nature and
structures of spacetime. Chapter 1 is devoted to an extensive partly new analysis of the law
of inertia. The underlying mathematical and geometrical structure of Newtonian spacetime is
presented from a four-dimensional point of view and some historical difficulties and
controversies - in particular the concepts of free particles and straight lines - are
critically analyzed while connections to projective geometry are also explored. The
relativistic extensions of the law of gravitation and its intriguing consequences are studied
in Chapter 2. This is achieved following the works of Weyl Ehlers Pirani and Schild by
adopting a point of view of the combined conformal and projective structure of spacetime.
Specifically Mach's fundamental critique of Newton's concepts of 'absolute space' and
'absolute time' was a decisive motivation for Einstein's development of general relativity and
his equivalence principle provided a new perspective on inertia. In Chapter 3 the very special
mathematical structure of Einstein's field equations is analyzed and some of their remarkable
physical predictions are presented. By analyzing different types of dragging phenomena Chapter
4 reviews to what extent the equivalence principle is realized in general relativity - a
question intimately connected to the 'new force' of gravitomagnetism which was theoretically
predicted by Einstein and Thirring but which was only recently experimentally confirmed and is
thus of current interest.
