The main topic of this series of talks is omega_1, and in particular, the theory of (capturing) construction schemes over omega_1 as introduced by S. Todorcevic. We will start by talking about certain kinds of construction schemes, namely the ones which are capturing (whose existence follows from Diamond), rho-capturing (whose existence follows from Club) , and Delta capturing (whose existence follows from CH). We will briefly discuss the effect that some of the usual forcing axioms have on these capturing schemes. Lastly, we will introduce some parametrized forcing axioms relative to capturing schemes and use them to settle some natural questions about gaps and almost disjoint families over omega. This is a Joint work with Osvaldo Guzman and Stevo Todorcevic.