The aim of this thesis is to understand the results of Björn, Björn, Gill and Shanmugalingam [BBGS], who give an analogue of the famous Trace Theorem for Sobolev spaces on the infinite K-ary tree and its boundary.  In order to do so, we investigate the properties of a tree as a metric measure space, namely the doubling condition and Poincaré inequality, and study the boundary in terms of geodesic rays as well as random walks. We review the definitions of the appropriate Sobolev and Besov spaces and the proof of the Trace Theorem in [BBGS].