  Einstein's general relativity is the best available theory of gravity. In
recent years, spectacular proofs of Einstein's theory have been conducted,
which have aroused interest that goes far beyond the narrow circle of
specialists. The aim of this work is to offer an elementary introduction to
general relativity. In this first part, we introduce the geometric concepts
that constitute the basis of Einstein's theory. In the second part we will use
these concepts to explore the curved spacetime geometry of general relativity.
