The electricity markets worldwide have distinctive particularities due to some political and historical reasons. However, principal guidelines of market design remain very similar. The main feature of deregulation is to introduce a competition into the generation, whereas the transmission network remains a natural monopoly. In this regard, the physical operation is separated from the economical functioning of the power system. In an open market environment, power supply becomes a competitive activity, hence traditional methods for power generation (like economic dispatch or unit commitment) need modifications. This thesis is devoted to the development of a comprehensive framework for the analysis and formulation of bidding strategies in a competitive market environment. The spot market concept is used as the basis for the modelling of a very general competitive market structure. It provides the solution for the multi-period auction dispatcher problem and for specifying the optimal bidding strategies. All the unique constraints under which electrical generators operate, including ramp rates, start-up and shut-down time restrictions and unit output limits are taken into account. Market design is challenged by multiple objectives to be satisfied. The solution of those multi-objective problems is searched often over the combined strategy space, and thus requires the simultaneous optimization of multiple parameters. The problem is formulated analytically using the Nash equilibria concept for games composed of large numbers of players having discrete and large strategy spaces. The solution methodology is based on a characterization of Nash equilibria in terms of minima of a function and relies on a meta-heuristic optimization approach to find these minima. Meta-heuristics are proven to be an efficient method of optima search in large scale multi-objective problems. Particularly, a genetic algorithm is proposed as a search engine, driven by an objective function that represents the evaluation of the solution in terms of Nash optimality. The approach is applied to compute Nash equilibria of the electricity markets and, based on the simulation results, its performances are discussed. It results from this thesis the development and implementation of the simulation tool to study and analyze different market scenarios. As an example, one can examine the strategic profit maximizing behavior of bidding generators, the effect of such behavior on the market prices, or to monitor the exercise of the market power. We have conducted a wide range of numerical studies; the results illustrate the robustness and the efficiency of the proposed hybrid evolutionary Nash search technique. As part of the thesis, the analysis of the market impact on the power grid operation is carried out. The methodology to eliminate the congestion caused by a pure economic dispatch is proposed based on the genetic algorithm.