This paper is devoted to the problem of providing control algorithms for the system of one spin 1/2 particle and two interacting spin frac 1/2 particles. The paper provides several improvements and new results with respect the previous papers [QC1]-[QC2], [QC5]-[QC6] and also summarizes the previous results obtained in these papers. The new contribution include 1) an analysis of the controllability of the system of two interacting spin 1/2 particles in the spirit of what was done in [QC2] for the single spin 1/2 particle 2) A proof that sinusoidal input fields used in Nuclear Magnetic Resonance are not only the minimum energy control fields, as it was shown in [QC1], but also the minimum time fields for the system of one spin 1/2 particle as well as the derivation of the minimum time controls for this system. 3) An improvement of the control algorithm based on decomposition of Lie groups that was previously presented in [QC5]. The algorithm is modified so that the parameters involved in the Lie group decomposition, which are necessary for the determination of the controls can be explicitly calculated analytically. This algorithm allows the steering of the system of two interacting spin 1/2 particles to any desired final configuration.