Robustness is the ability of networks to avoid malfunction. Networks could be subject to failures, viruses, removals of links and other attacks. There are several researches about how to measure or improve the network robustness in large networks by doing small modifications such as adding new links or nodes. A small network modification is required because setting up links in real-world networks is expensive. Different metrics can be used in order to measure robustness. This project focuses on the algebraic connectivity as the way of measuring connectivity. The main statement is that the larger the algebraic connectivity is, the more difficult to disconnect the network is. The goal of this project is to design strategies to add a number (or a certain percentage) of links to a network such that the algebraic connectivity can be increased the most. Insights may come from results in mathematics, or the strategies for adding one link. In summary, the idea consists of optimizing a network in terms of algebraic connectivity by means of link additions. Finally, different strategies will be evaluated on different types of networks such as the Barabasi-Albert power law graphs or Erdös-Rényi random graphs.