Abstract:
This dissertation intends to study the Algebra by Rafael Bombelli (1572) trying to integrate it in the whole of the algebraic knowledge related to that time and concomitantly to evidence its particularities.
The main contents from Bombelli?s study are focalized in this study:

- the insertion of the imaginary numbers and its operative rules;
- the resolution of equations, from the first to the fourth degrees, with special emphasis to the resolution of the irreducible cubic equation by Cardano-Tartaglia?s formula and to the first and complete study of the fourth degree equations;
- the insertion of the concept of continuous fraction when using to calculate the square root ?s approached values from a non- square number.
- the first translation to a western language - the Italian one - of an ample numbers of problems from Diofanto?s Arithmetica in which we stress the influence of this Greek mathematician on Bombelli?s studies;
- the utilization of the unitary segment on the geometric definition of the basic arithmetical operations, just as Descartes will adopt later;
- the resolution of geometric problems whose constructions are based on the algebraic resolution of those ones;
- the approach of an angle trisection problem and its relation with the irreducible cubic equation.

We intend to contextualize the several themes related in this study, using original documents and stressing the relations among several generations of mathematicians and, in particular, the Portuguese one ? Pedro Nunes.
Add to the scientific aspects we mark out the Bombelli?s didactic concerns that we consider so interesting, and can be the source of reflection and inspiration for our professional activity as teachers.