Abstract: A "typical" continuous curve on a plane looks like a path of Brownian motion. A natural next question we might ask is "what does a "typical" continuous 2d-surface looks like?" One of the ways to construct such a model is to find a discrete object and consider a scaling limit of it (analogous to considering a scaling limit of a random walk to construct Brownian motion). Such objects are called random planar maps - planar multi-graphs embedded in a sphere or a plane. Of course, similarly to random walks, there are many other reasons why these discrete objects are interesting. In these two talks we will consider several ways of defining random planar maps and a measure on them, connections with random walks and random trees. Finally, in the remaining time I will try to mention several highlights of the field in connection with combinatorics, percolation theory, scaling limits, and Ergodic theory.