Geometry, space-time and gravitation: relating basic concepts of general relativity

The theory of general relativity is formulated in a precise, but very complex, mathematical formalism. In spite of being necessary, this mathematical rigour may become an insurmountable obstacle. Notwithstanding this theory is grounded in principles and ideas accessible to anyone. We will try to construct a logical path between the ideas that helped Einstein formulate general relativity and connect concepts at first glance so apart as geometry, curved space-times and gravitation. We have chosen to favour a constructive approach at the expense of lack of accuracy from a historical perspective. We hope to clarify the main concepts and principles involved in general relativity focusing mainly on its epistemological and philosophical implications.