Slopes and periods of connections

For a smooth algebraic variety X over C, the periods of X are certain complex numbers obtained by integration of differential forms on X along topological cycles drawn on X_an. As shown by Deligne, algebraic regular connections on X give rise to periods, and when varying in families, periods satisfy a differential equation with regular singularities. This talk is an introduction to the ideas and notions that revolve around these results. We will also explain a recent progress on what can be said for periods of general algebraic connections. No prerequisite on D-modules is necessary to follow this talk.