The precise positioning of the mitotic spindle to the cell center during mitosis is a fundamental process for chromosome segregation and the division plane definition. Despite its importance, the mechanism for spindle centering remains elusive. To study this mechanism, the dynamic of the microtubules was characterized at the bulk and at the cortex in the C. elegans embryo. Then, this dynamic was correlated to the centering forces of the spindle that were studied by applying calibrated magnetic forces via super-paramagnetic beads inserted into the cytoplasm of one- and two-cell C. elegans embryos. Finally, these results were confronted with the different centering models: cortical pushing model, cortical pulling model and the cytoplasmic pulling model. This thesis shows that: (i) The microtubules dynamic of the spindle aster is controlled spatially in the C. elegans embryo, with not rescues and catastrophes in the cytoplasm but in the centrosome and the cortex, respectively. (ii) The centering mechanism of the spindle behaved roughly as a damped spring with a spring constant of 18 12 pN/ m and a drag coefficient of 127 65 pN s/ m (mean SD). This viscoelastic behavior is evidence of a centering force that recovers and/or maintains the position of the spindle in the cell center. (iii) It seems to be two mechanisms that recover/maintain the spindle position. A fast one that may work for transient displacements of the spindle and a slow one that work over large and long perturbations. (iv) The centering forces scale with the cell size. The centering forces are higher in the two-cell embryo. This result argues against a centering mechanism mediated by cytoplasmic factors. It seems to be a limit for the relation of centering force to size, as the forces found in the four-cell embryo are comparable to the single-cell ones. (v) The centering forces scale with the amount of microtubules in the cell. This strengthens the belief that the microtubules are the force transmission entities of the centering mechanism. (vi) The boundary conditions are important to maintain the centering forces. A transient residency time of microtubules at the cortex, which is controlled by cortical catastrophe factors, is indispensable for a proper force transmission by the microtubules. (vii) The elimination of cortical catastrophe factors provides evidence for microtubules buckling, which is taken as a proof of polymerization forces. (viii) The cortical pulling forces mediated by the gpr-1/2 pathway do not seem to be involved in centering and it is proposed they are present in the cell for off-center positioning purposes. (ix) The forces generated by vesicle transport are enough to displace the spindle and they are suggested to be auxiliary forces to centering. (x) The forces associated with the spindle change dramatically during cell division. From metaphase to anaphase the forces associated with the spindle scale up to five times. This behavior was consistent during the development of the embryo as the same pattern was observed in the one-, two- and four-cell embryo. (xi) The higher forces found during anaphase are not cortical pulling (via pgr-1/2 pathway) depended, and it is proposed the spindle is `immobilised' by tethering or by an unknown cortical pulling pathway. To this date, this thesis presents the most complete in-vivo measurements of the centering forces in association with the microtubules dynamics. Taken together the results constrain molecular models of centering. This thesis concludes that most probably the predominant forces of the spindle centering mechanism during mitosis are generated by astral microtubules pushing against the cortex. Additionally, this thesis presents the most complete map of forces during cell division during development, which will prove to be indispensable to understand the changes the spindle undergoes when it changes its function.