In selecting the boundary of a signal constellation used for data transmission, the objective is to minimize the average energy of the set for a given number of points from a given packing. Reduction in the average energy because of using the region 𝒞 as the boundary instead of a hypercube is called the shape gain of 𝒞. The price to be paid for shaping is:​ (i) an increase in the factor CER_s (Constellation-Expansion-Ratio), (ii) an increase in the factor PAR (Peak-to-Average-power-Ratio), and (iii) an increase in the addressing complexity. In this thesis, the structure of the region which optimizes the tradeoff between the shape gain and the CER_s and also between the shape gain and the PAR in a finite dimensional space is found. Analytical expressions are derived for the optimum tradeoff. The optimum shaping region can be mapped to a hypercube truncated within a simplex. This mapping has properties which facilitate the addressing of the signal points. We introduce several addressing schemes with low complexity and good performance. The concept of the unsymmetrical shaping is discussed. This is the selection of the boundary of a constellation which has different values of power along different dimensions. The rate of the constellation is maximized subject to some constraints on its power spectrum. This spectral shaping also involves the selection of an appropriate basis (modulating waveform) for the space. Finally, we discuss the selection a signal constellation of signaling over a partial-response channel. In the continuous approximation, we introduce a method to select the nonempty dimensions. This method is based on minimizing the degradation caused by the channel memory. In the discrete case, shaping and coding depend on each other. In this case, a combined shaping and coding method is used. This concerns the joint selection of the shaping and coding to minimize the probability of the symbol error.