  We are experiencing a period of extreme intellectual effervescence in the
area of cosmology. A huge volume of observational data in unprecedented
quantity and quality and a more consistent theoretical framework propelled
cosmology to an era of precision, turning the discipline into a cutting-edge
area of contemporary science. Observations with type Ia Supernovae (SNe Ia),
showed that the expanding Universe is accelerating, an unexplained fact in the
traditional decelerated model. Identifying the cause of this acceleration is
the most fundamental problem in the area. As in the scientific renaissance, the
solution will guide the course of the discipline in the near future and the
possible answers (whether dark energy, some extension of general relativity or
a still unknown mechanism) should also leverage the development of physics. In
this context, without giving up a pedagogical approach, we present an overview
of both the main theoretical results and the most significant observational
discoveries of cosmology in the last 100 years. The saga of cosmology will be
presented in a trilogy. In this article (Part I), based on the articles by
Einstein, de Sitter, Friedmann, Lema\^itre and Hubble, we will describe the
period between the origins of cosmology and the discovery of Universal
expansion (1929). In Part II, we will see the period from 1930 to 1997, closing
with the old standard decelerated model. The Part III will be entirely devoted
to the accelerated model of the universe, the cosmic paradigm of the XXI
century.
