The theme of this course is the construction of algebraic points on elliptic curves from special points and higher-dimensional cycles on Shimura varieties and closely related objects. The lecturers will provide background for, explain, and, time permitting, expand further on the results that are proven in the two works in progress: 1.- M. Bertolini, H. Darmon, and K. Prasanna, "Generalised Heegner cycles and p-adic Rankin L-series"; 2.- M. Bertolini, H. Darmon, and K. Prasanna, "Chow-Heegner points on CM elliptic curves and values of p-adic L-series".