This PhD thesis deals with some particular aspects of the algebraic systems resolution. Firstly, we introduce a way of minimizing the number of additive variables appearing in an algebraic system. For this, we make use of two invariants of variety introduced by Hironaka: the ridge and the directrix. Then, we propose fast arithmetic routines, the so-called relaxed routines, for p-adic integers. These routines allow us, then, to solve efficiently an algebraic system with rational coefficients locally, i.e. over the p-adic integers. In a fourth part, we are interested in the factorization of a bivariate polynomial, which is at the root of the decomposition of hypersurfaces into irreducible components. We propose an algorithm reducing the factorization of the input polynomial to that of a polynomial whose dense size is essentially equivalent to the convex-dense size of the input polynomial. In the last part, we consider real algebraic systems solving in average. We design a probabilistic algorithm computing an approximate complex zero of the real algebraic system given as input.
