Introduction.- Part 1. The Sierpiński Gasket.- Definition and General Properties.- The Laplace Operator on the Sierpiński Gasket.- Harmonic Functions on the Sierpiński Gasket.- Part 2. The Apollonian Gasket.- Introduction.- Circles and Disks on Spheres.- Definition of the Apollonian Gasket.- Arithmetic Properties of Apollonian Gaskets.- Geometric and Group-Theoretic Approach.- Many-Dimensional Apollonian Gaskets.- Bibliography.